Module 01: Kinematics

Question 1

Lessson 1.1 - Speed and Velocity and Acceleration

Define Mechanics:

Answer 1

Mechanics is the study of the motion of objects, and the related concepts of force and energy.

Question 2

Lessson 1.1 - Speed and Velocity and Acceleration

What are the two fields of mechanics?

Answer 2

1. Kinematics (description of how objectives move)
2. Dynamics (deals with the forces and why objects move as they do)

Question 3

Lessson 1.1 - Speed and Velocity and Acceleration

What is translational motion?

Answer 3

Objects that move without rotating

Question 4

Lessson 1.1 - Speed and Velocity and Acceleration

What is the idealized particle?

Answer 4

• mathematical point with no spatial size (no size)
• Can only go through translational motion

Question 5

Lessson 1.1 - Speed and Velocity and Acceleration

What is a reference frame and why is it important?

Answer 5

Any measurement of position, distance, or speed needs a reference frame.

• Important to specify
  
  • Need to say “with respect to Earth” to avoid confusion

Question 6

Lessson 1.1 - Speed and Velocity and Acceleration

What are important aspects of the motion of an object?

Answer 6

(1) SPEED and (2) DIRECTION of motion

Question 7

Lessson 1.1 - Speed and Velocity and Acceleration

Define distance and displacement

Answer 7

Distance: Change in position of the object

Displacement: How far the object is from its starting point

Question 8

Lessson 1.1 - Speed and Velocity and Acceleration

What are the components of a vector? Does displacement qualify?

Answer 8

Vectors have both (1) MAGNITUDE and (2) DIRECTION (and displacement qualifies)

Question 9

Lessson 1.1 - Speed and Velocity and Acceleration

What does the sign of movement along a line (vector in one dimension)?

Question 10

Lessson 1.1 - Speed and Velocity and Acceleration

What is the formula for displacement?

Answer 10

Δx = x₂ - x₁

• ­­Δx = Displacement
• x₂ - x₁ = Position Two minus Position One

Question 11

Lessson 1.1 - Speed and Velocity and Acceleration

What does “speed” refer to?

Answer 11

How far an object travels in a given amount of time

Question 12

Lessson 1.1 - Speed and Velocity and Acceleration

What is average speed?

Answer 12

Total distance traveled along its path is divided by the time it takes to travel the distance

Question 13

Lessson 1.1 - Speed and Velocity and Acceleration

What is the difference between velocity and speed?

Answer 13

• Speed: positive number (with units)
• Velocity: signify both (1) magnitude and (2) direction [meaning its a vector]
• Furthermore, the average velocity is displacement over time (rather than distance)

Question 14

Lessson 1.1 - Speed and Velocity and Acceleration

What is average velocity?

Answer 14

• Displacement divided by the elapsed time

Question 15

Lessson 1.1 - Speed and Velocity and Acceleration

When does average speed and average velocity have the same magnitude?

Answer 15

If the motion of an object is along a straight line and in the same direction, the magnitude of displacement is equal to the total path length. In that case, the magnitude of the average velocity is equal to the average speed.

Question 16

Lessson 1.1 - Speed and Velocity and Acceleration

Define instantaneous velocity (and the formula).

Answer 16

• The average velocity over an infinitesimally short time interval*
• Evaluated in the limit of Δt becomes extremely small (approaching zero)

Question 17

Lessson 1.1 - Speed and Velocity and Acceleration

Why is the instantaneous speed always equal to the magnitude of the displacement?

Answer 17

because the distance traveled and the magnitude of the displacement becomes the same when they are infinitesimally small

Question 18

Lessson 1.1 - Speed and Velocity and Acceleration

When the average velocity and the velocity equal to each other?

Answer 18

When an object moves at a uniform velocity during a particular time

Question 19

Lessson 1.1 - Speed and Velocity and Acceleration

What is acceleration?

Answer 19

Specifies how rapidly the velocity of an object is changing

SI units of acceleration: m/s²

Question 20

Lessson 1.1 - Speed and Velocity and Acceleration

What is the average acceleration?

Answer 20

Velocity is divided by the time taken to make this change.

Question 21

Lessson 1.1 - Speed and Velocity and Acceleration

What is instantaneous acceleration?

Answer 21

Analogy to instantaneous velocity as the average acceleration over an infinitesimally short time interval at a given time:

Question 22

Lessson 1.1 - Speed and Velocity and Acceleration

What is deceleration?

Answer 22

• Object is slowing down
• Not mean that acceleration is necessarily negative

Question 23

Lessson 1.1 - Speed and Velocity and Acceleration

What is the formula for displacement when the acceleration is constant?

Answer 23

Δx = v_i Δt + 1/2 a (Δt)²

• Δx: displacement
• v_i: initial velocity
• Δt: change in time
• a: acceleration (must be constant)

Question 24

Lessson 1.1 - Speed and Velocity and Acceleration

What direction is acceleration when the velocity is negative?

Answer 24

Positive (acceleration is always the opposite direction than velocity)

Question 25

# Lesson 1.2 - Motion at Constant Acceleration, Freefalling Objects, and Graphical Analysis When is motion in a strait line?

Answer 25

When acceleration is constant.

Question 26

# Lesson 1.2 - Motion at Constant Acceleration, Freefalling Objects, and Graphical Analysis What happens at constant acceleration?

Answer 26

1. Motion is in a straight line 2. Instantaneous and average acceleration are equal

Question 27

# Lesson 1.2 - Motion at Constant Acceleration, Freefalling Objects, and Graphical Analysis How does the notation change when discussing constant acceleration?

Answer 27

_Initial time_ at zero: t_0. Therefore, t₁ = t₀ = 0 _Elaposed time_: t₂ = t Initial position (x₁ = x₀) and Initial velocity (v1 = v₀) Hence,

Question 28

# Lesson 1.2 - Motion at Constant Acceleration, Freefalling Objects, and Graphical Analysis What is the average velocity over the time interval t - t₀:

Answer 28

Question 29

# Lesson 1.2 - Motion at Constant Acceleration, Freefalling Objects, and Graphical Analysis Formula to solve for the velocity of an object after any time elapsed when we are given the object's constant acceleration:

Answer 29

v = v₀ + at

Question 30

# Lesson 1.2 - Motion at Constant Acceleration, Freefalling Objects, and Graphical Analysis Formula to determine the average velocity using initial and final velocity: (assuming constant acceleration)

Answer 30

Question 31

# Lesson 1.2 - Motion at Constant Acceleration, Freefalling Objects, and Graphical Analysis Formula to find the position of *x* after a time *t* when it undergoes constant acceleration:

Answer 31

Question 32

# Lesson 1.2 - Motion at Constant Acceleration, Freefalling Objects, and Graphical Analysis What are the four Kinematic Equations for Constant Acceleration?

Answer 32

* Only valid when a = constant. * Set x₀=0 for simplicity * x = position (not distance) * Displacement: x-x₀

Question 33

# Lesson 1.2 - Motion at Constant Acceleration, Freefalling Objects, and Graphical Analysis What is the problem-solving strategy for physics?

Answer 33

1. **Read** the question 2. **Decide** what object you are going to study, and for what time interval. (ex. t = 0) 3. Draw a **diagram** of the situation 4. Write down the "**knows**" or "**givens**" and what you *want* to know 5. Think about the **principles of physics** apply in the problem 6. Consider which **equations** are related to the quantities involved. 7. Carry out the **calculations** in its a numerical problem (Keep one or two extra digits in the calculations) 8. Think about the result: IS IT REASONABLE? 9. Always keep track of UNITS.

Question 34

# Lesson 1.2 - Motion at Constant Acceleration, Freefalling Objects, and Graphical Analysis Describe the acceleration of a freefalling object:

Answer 34

Example of UNIFORM ACCELERATION * Used to believe that heavier objects fall faster than lighter objects and that speed is proportional to how heavy an object is * Truth: **The Speed of a falling object is not proportional to its mass!** * Galileo's contribution to the understanding of motion of falling objects: * At a given location on the Earth and in the absence of air resistance, all objects fall with the same constant acceleration*

Question 35

# Lesson 1.2 - Motion at Constant Acceleration, Freefalling Objects, and Graphical Analysis Why is Galileo the "father of modern mathematics?"

Answer 35

Not for the content of his science by for his new methods of doing science ((idealization and simplification, mathematization of theory) Ex. Realized that freefalling objects have a uniform acceleration

Question 37

# Lesson 1.2 - Motion at Constant Acceleration, Freefalling Objects, and Graphical Analysis What is the acceleration due to gravity?

Answer 37

At a given location on the Earth and in the absence of air resistance, all objects fall with the same constant acceleration - *Galileo* Magnitude: **g = 9.80m/s²** (1) Vector and (2) Direction is downwards towards earth

Question 39

# Lesson 1.2 - Motion at Constant Acceleration, Freefalling Objects, and Graphical Analysis How do equations change when dealing with free-falling objects?

Answer 39

* a = g = 9.80m/s² * y₀ takes the place of x₀ (since the motion is vertical)

Question 40

# Lesson 1.2 - Motion at Constant Acceleration, Freefalling Objects, and Graphical Analysis Why is the trowing action not part of acceleration?

Answer 40

During the throw, the hand is touching the ball and the acceleration is unknown to us. Only consider when the ball is in the air and the acceleration is equal to *g .*

Question 41

# Lesson 1.2 - Motion at Constant Acceleration, Freefalling Objects, and Graphical Analysis How is acceleration of rockets and fast airplanes measured?

Answer 41

Multiples of g. Ex. a Plane pulling out of a dive and undergoing 3 g's has an acceleration of (3.00)(9.80m/s²)

Question 42

# Lesson 1.2 - Motion at Constant Acceleration, Freefalling Objects, and Graphical Analysis What is the average velocity of an object (based on a graph)?

Answer 42

The Average Velocity of an object during any time interval ▲t = t₂ - t₁ *is equal to the slope of the straight line (or chord) connecting the two points.*

Question 43

# Lesson 1.2 - Motion at Constant Acceleration, Freefalling Objects, and Graphical Analysis What is the instantaneous velocity (from a graph)?

Answer 43

The Instantaneous Velocity equals the slope of the tangent to the curve of x vs. t at any chosen point.

Question 44

What is the velocity-time graph for an object thrown (1) upwards, (2) downwards, and (3) released from rest?

Answer 44

* Object thrown downwards: linear graph with a negative intercept and a negative slope * Object thrown upwards: linear velocity-time graph with a positive intercept and a negative slope * Object released from rest: linear slope with an intercept at zero and a negative slope

Question 45

# Lesson 1.3 - Vector Addition What is a vector quantity?

Answer 45

Direction as well as the magnitude

Question 46

# Lesson 1.3 - Vector Addition What is a scalar quantity?

Answer 46

Quantities have no direction associated with them (mass, time, and temperature)

Question 47

# Lesson 1.3 - Vector Addition How can scalar quantities be added?

Answer 47

* Added using arithmetic (also be used for vectors if they have the same direction) * Total = called the *net* or *resultant* displacement

Question 48

# Lesson 1.3 - Vector Addition What is the method to determining the resultant displacement (when directional quantities are perpendicular)?

Answer 48

* Use the pythagorean theorem

Question 49

# Lesson 1.3 - Vector Addition What is the vector equation?

Answer 49

Adding two vectors: the magnitude of the resultant vector is not equal to the sum of the magnitudes of the two separate vectors Rules: 1. Draw one vector D1 to scale 2. Draw D2 to scale, placing the tail at the tip of the second vector 3. The arrow drawn from the tail of the first vector to the tip of the second vector represents the sum (or resultant) of the two vectors

Question 50

# Lesson 1.3 - Vector Addition What is the tail-to-tip method for adding vectors?

Answer 50

Note that vectors can be moved parallel to themselves on paper 1. Draw one vector D1 to scale 2. Draw D2 to scale, placing the tail at the tip of the second vector 3. The arrow drawn from the tail of the first vector to the tip of the second vector represents the sum (or resultant) of the two vectors

Question 51

# Lesson 1.3 - Vector Addition What is the parallelogram method to add vectors?

Answer 51

1. Vectors drawn from a common origin and a parallelogram is constructed using two vectors as adjacent sides 2. A diagonal drawn from the common origin

Question 52

# Lesson 1.3 - Vector Addition What is a negative vector?

Answer 52

(1) Same magnitude but (2) opposite direction - V

Question 53

# Lesson 1.3 - Vector Addition How do you add two vectors?

Answer 53

The difference between two vectors:

Question 54

# Lesson 1.3 - Vector Addition How can you multiply two vectors?

Answer 54

Vector can be multiplied by a scalar (c) Product: ***cV*** * Same direction as V and the magnitude of cV

Question 55

# Lesson 1.3 - Vector Addition What are components?

Answer 55

V: sum of two vectors which are the components of the original vector Process of finding the components: *resolving the vector into its components* * *Vector components:* both magnitude and direction * *Scalar components:* just magnitude

Question 56

# Lesson 1.3 - Vector Addition How do you add vectors?

Answer 56

1. Resolve each vector into its components 2. Hence, V_RY = V_1Y + V_2Y (*not add x and y components together)*

Question 57

The sum of two vectors of fixed magnitudes has the greatest magnitude when the angle between these two vectors is:

Answer 57

0°

Question 58

# Lesson 1.4 - Projectile Motion What is **projectile motion**?

Answer 58

*Ex*: golf ball, the Earth's surface, and batted baseball ## Footnote **Action that is taking place in two dimensions if there is no wind**

Question 59

# Lesson 1.4 - Projectile Motion What is **air resistance's** role in projectile motion?

Answer 59

* Often important (many cases its effect can be ignored) * Ignore it in the following analysis *We consider only its motion after it has been projected, and before it lands or is caught - only analyse when it is moving freely through the air under the action of gravity alone.* Acceleration of the object due to gravity: **g = 9.80 m/s²**

Question 60

# Lesson 1.4 - Projectile Motion How will the time between an object dropped vertically and horizontally differ?

Answer 60

An object projected horizontally will reach the ground in the **same time** as an object dropped vertically Vertical motion in both cases are the same

Question 61

# Lesson 1.4 - Projectile Motion What is the formula for the vertical and horizontal components of a ball dropped from a table?

Answer 61

y = y₀ + v_y0 + 1/2 a_yt² x = v_x0t + 1/2 a_xt² = v_x0t

Question 62

# Lesson 1.4 - Projectile Motion What are the General Kinematic Equations for Constant Acceleration in Two Dimensions

Answer 62

Question 63

# Lesson 1.4 - Projectile Motion What are the Kinematic Equations for Projectile Motion?

Answer 63

Question 64

# Lesson 1.4 - Projectile Motion If projection angle Θ₀ is chosen relative to the +x axis then:

Answer 64

Question 65

# Lesson 1.4 - Projectile Motion What are the steps to solving Projectile Motion Questions?

Answer 65

# 1. Read carefully 2. Draw a careful diagram showing what is happening 3. Choose an origin and an xy coordinate system 4. Decide on a time interval 5. Examine the horizontal (x) and vertical (y) motions separately. *If you are given the initial velocity, you may want to resolve it into x and y components* 6. List the known and unknown quantities: a_x = 0 a_y = -g or +g *(Remember that v_x never changes throughout the trajectory and v_y = 0 at the highest point of any trajectory that returns downwards* 7. Apply the relevant equations

Question 66

What is the level horizontal range equations?

Answer 66

Question 67

What is **kinematics**?

Answer 67

a study of how things move, without regard to the cause

Question 68

What is the difference between position and displacement?

Answer 68

**Position**: * Location in space * Scalar quantity **Displacement**: * Change in position * Vector quantity

Question 69

What is the velocity (instantaneous and average)?

Answer 69

🔬 **_Velocity_**: Rate of change of an object’s displacement * **Average Velocity:** displacement/time v_a =(v₀+v₁)/2 * **Instantaneous Velocity**: v = dx/dy * **Displacement** related to the (constant) velocity: x=x₀+vt

Question 70

What are particle models and motion diagrams?

Answer 70

**Particle model**: single point on the page **Motion diagram**: position of an object at equally-spaced time intervals * Unequal spacing between successive points indicate that velocity is changing * Equal spacing between points indicate time

Question 71

What is a net arrow?

Answer 71

**Net Arrow**: difference in length between two successive arrows on a motion diagram indicates the relative magnitude and direction of the change in velocity

Question 72

How does the direction of acceleration and velocity relate?

Answer 72

1. Acceleration points same direction as the velocity vector: **velocity increases** 2. Acceleration points in the opposite direction as the velocity: **velocity decreases**

Question 73

What is instantaneous acceleration?

Answer 73

**Found by reducing the time elapsed to a very small value** * Derivative for velocity: a = dv/dt * Second derivative for dispalcement: a_x=d²x/dt²

Question 74

What are the kinematic equations?

Answer 74

where x is the final position, x₀ is the initial position, v is the final velocity, v₀ is the initial velocity, a is acceleration, and t is the elapsed time.

Question 75

What is a free-falling object's acceleration?

Answer 75

Constant accelerating equal to the acceleration due to gravity

Question 76

Describe the motion and acceleration of a ball moving up and down a ramp:

Answer 76

Linear acceleration of an object on a ramp = component of the acceleration due to gravity that points parallel to the slope of the incline: **a=g sinθ** Ball given an initial push and rolled up a ramp slows down, stops momentarily at the turning point, then starts to speed up and roll back down _Turning point_: location where the velocity of a moving object with constant acceleration is momentarily zero * Before the turning point is reached, the velocity and acceleration point in opposite directions like when a ball is tossed into the air and starts slowing down. * After the turning point, the velocity and acceleration point in the same direction, like when the ball tossed into the air falls back toward the ground.

Question 77

What is projectile motion?

Answer 77

🔬 **Projectile Motion**: motion of an object under the influence of gravity alone * Two-dimensional motion requires the kinematic equations separated in each dimension: * Includes free-falling objects in one dimension and those following parabolic motion

Question 78

What are free-falling objects? How do they compare to objects in a parabolic path?

Answer 78

**Free-Falling Objects**: * no horizontal velocity or acceleration * moves only in the vertical direction under the influence of gravity * Angle of lauch determines whether an object is free-falling or parabolic **Parabolic Path**: has some initial velocity in the horizontal direction

Question 79

What is a trajectory?

Answer 79

path of an object in the (x,y) plane - straight, vertical line or a parabola

Question 80

How does horizontal and vertical motion compare?

Answer 80

Horizontal and vertical motion are independent Factor connecting horizontal and vertical components: Time **Horizontal Motion:** * Horizontal direction has no acceleration * Horizontal velocity remains constant * Velocity has the same magnitude at each vertical position **Vertical Motion**: * Vertical direction has acceleration due to gravity * Vertical velocity changes continuously (due to acceleration due to gravity) * Two times will be calculated when the object travels: Objects travel _upwards_ with specified velocity in the positive direction Object travels _downwards_ with the same magnitude velocity in the negative direction

Question 81

What is the range?

Answer 81

* Change in the initial angle or intial velocity of a projectile changes the range and the maximum height * When air resistance is ignored, the mass and shape of the projectile do not affect the trajectory, range, or maximum height of the projectile

Question 82

# Lesson 1.1 Questions **1.** (I) If you are driving 95 km/h along a straight road and you look to the side for 2.0s, how far do you travel during this inattentive period?

Answer 82

Question 83

# Lesson 1.1 Questions **3.** (I) A particle at t₁ = –2.0 s is at x₁ = 4.8 cm and at t₂ = 4.5 s is at x₂ = 8.5 cm. What is its average velocity over this time interval? Can you calculate its average speed from these data? Why or why not?

Answer 83

Question 84

# Lesson 1.1 Questions **7.** (II) You are driving home from school steadily at 95 km/h for 180 km. It then begins to rain and you slow to 65 km/h. You arrive home after driving 4.5 h. (a) How far is your hometown from school? (b) What was your average speed?

Answer 84

Question 85

# Lesson 1.1 Questions **11.** (II) A car traveling 95 km/h is 210 m behind a truck traveling 75 km/h. How long will it take the car to reach the truck?

Answer 85

210 m = 0.21 km F(x) = truck’s distance & G(x) = car’s distance F(x) = 75x + 0.21 (where x is hours and F(x) is km) G(x) = 95x (where x is hours and G(x) is km) Determine where the car’s distance is equal to truck’s distance, so F(x) = G(x): F(x) = G(x) 75x + 0.21 = 95x 0.0105 = x Therefore, the car needs approximately **0**.**0105 hours** or **38 second**s to reach the truck.

Question 86

# Lesson 1.1 Questions **13.** (II) Two locomotives approach each other on parallel tracks. Each has a speed of 155 km/h with respect to the ground. If they are initially 8.5 km apart, how long will it be before they reach each other? (See Fig. 2–35.)

Answer 86

Question 87

# Lesson 1.1 Questions **19.** (II) A sports car moving at constant velocity travels 120 m in 5.0 s. If it then brakes and comes to a stop in 4.0 s, what is the magnitude of its acceleration (assumed constant) in m/s², and in g’s (g = 9.80 m/s²)?

Answer 87

Question 88

# Lesson 1.2 Questions **23**. (I) A car accelerates from 14 m/s to 21 m/s in 6.0 s. What was its acceleration? How far did it travel in this time? Assume constant acceleration.

Answer 88

Question 89

# Lesson 1.2 Questions **25**. (II) A baseball pitcher throws a baseball with a speed of 43 m/s. Estimate the average acceleration of the ball during the throwing motion. In throwing the baseball, the pitcher accelerates it through a displacement of about 3.5 m, from behind the body to the point where it is released (Fig. 2–37).

Answer 89

Therefore, the acceleration of the ball during the throwing motion is **264 m/s²**.

Question 90

# Lesson 1.2 Questions **29**. (II) A car traveling at 95 km/h strikes a tree. The front end of the car compresses and the driver comes to rest after traveling 0.80 m. What was the magnitude of the average acceleration of the driver during the collision? Express the answer in terms of “g’s,” where 1.00 g = 9.80 m/s².

Answer 90

Therefore, the magnitude of the average acceleration is equal to **44 g’s**.

Question 91

# Lesson 1.2 Questions **\* 31**. (II) Determine the stopping distances for an automobile going a constant initial speed of 95 km/h and human reaction time of 0.40 s: (a) for an acceleration a = –3.0 m/s²; (b) for a = –6.0 m/s².

Answer 91

Therefore, the stopping distance is (a) **127 m** and (b) **69 m**.

Question 92

# Lesson 1.2 Questions **33**. (II) A 75-m-long train begins uniform acceleration from rest. The front of the train has a speed of 18 m/s when it passes a railway worker who is standing 180 m from where the front of the train started. What will be the speed of the last car as it passes the worker? (See Fig. 2–38.)

Answer 92

Therefore, the speed of the final cart as it passes the worker is **21 m/s**.

Question 93

# Lesson 1.2 Questions **35**. (II) A runner hopes to complete the 10,000-m run in less than 30.0 min. After running at constant speed for exactly 27.0 min, there are still 1200 m to go. The runner must then accelerate at 0.20 m/s² for how many seconds in order to achieve the desired time?

Answer 93

Therefore, the runner needs to accelerate for approximately **6.3 seconds** to end in less than 30.0 minutes.

Question 94

# Lesson 1.2 Questions **39**. (I) A stone is dropped from the top of a cliff. It is seen to hit the ground below after 3.55 s. How high is the cliff?

Answer 94

Therefore, the cliff is **61.8 m** high.

Question 95

# Lesson 1.2 Questions **41**. (II) A ball player catches a ball 3.4 s after throwing it vertically upward. With what speed did he throw it, and what height did it reach?

Answer 95

Therefore, the speed he threw it with is **17 m/s** and it reached a height of **14** **m**.

Question 96

# Lesson 1.3 Questions **1.** (I) A car is driven 225 km west and then 98 km southwest (45°). What is the displacement of the car from the point of origin (magnitude and direction)? Draw a diagram.

Answer 96

tan Θ = 69.3/302 Θ = 13°

Question 97

# Lesson 1.3 Questions **5.** (II) V is a vector 24.8 units in magnitude and points at an angle of 23.4° above the negative x axis. (a) Sketch this vector. (b) Calculate V_x and Vy. (c) Use Vx and Vy to obtain (again) the magnitude and direction of V. [Note: Part (c) is a good way to check if you’ve resolved your vector correctly.]

Answer 97

Question 98

# Lesson 1.3 Questions **7.** (II) Figure 3–33 shows two vectors, A and B, whose magnitudes are A = 6.8 units and B = 5.5 units. Determine C if (a) C = A +B (b) C = A – B, (c) C = B – A. Give the magnitude and direction for each.

Answer 98

Question 99

# Lesson 1.3 Questions **15.** (II) The summit of a mountain, 2450 m above base camp, is measured on a map to be 4580 m horizontally from the camp in a direction 38.4° west of north. What are the components of the displacement vector from camp to summit? What is its magnitude? Choose the x axis east, y axis north, and z axis up.

Answer 99

Question 100

# Lesson 1.4 Questions **17.** (I) A tiger leaps horizontally from a 7.5-m-high rock with a speed of 3.0 m/s. How far from the base of the rock will she land?

Answer 100

Question 101

# Lesson 1.4 Questions **19.** *(Edited)* (II) Estimate by what factor a person can jump farther on the Moon as compared to the Earth if the takeoff speed and angle are the same. The acceleration due to gravity on the Moon is one-sixth what it is on Earth.

Answer 101

Question 102

# Lesson 1.4 Questions **25.** *(Edited)* (II) A grasshopper hops along a level road. On each hop, the grasshopper launches itself at angle q₀ = 45° and achieves a range R = 0.80 m. What is the average horizontal speed of the grasshopper as it hops along the road? Assume that the time spent on the ground between hops is negligible.

Answer 102

Question 103

# Lesson 1.4 Questions **31.** (II) A rescue plane wants to drop supplies to isolated mountain climbers on a rocky ridge 235 m below. If the plane is traveling horizontally with a speed of 250 km/h (69.4 m/s), how far in advance of the recipients (horizontal distance) must the goods be dropped (Fig. 3–38)?

Answer 103

Question 104

# Module 01 Exams If, in a parallel universe, π has the value 3.14149, express π in that universe to four significant figures. 1. 3.1415 2. 3.141 3. 3.142 4. 3.1414

Answer 104

2. 3.141

Question 105

# Module 01 Exams Add 3685 g and 66.8 kg and express your answer in milligrams (mg). 1. 7.05 × 10⁵ mg 2. 7.05 × 10⁴ mg 3. 7.05 × 10⁷ mg 4. 7.05 × 10⁶ mg

Answer 105

3. 7.05 × 10⁷ mg

Question 106

# Module 01 Exams The length and width of a rectangle are 1.125 m and 0.606 m, respectively. Multiplying, your calculator gives the product as 0.68175. Rounding properly to the correct number of significant figures, the area should be written as 1. 0.6818 m². 2. 0.68 m². 3. 0.682 m². 4. 0.68175 m². 5. 0.7 m².

Answer 106

3. 0.682 m².

Question 107

# Module 01 Exams How many nanoseconds does it take for a computer to perform one calculation if it performs 6.7 \* 10⁷ calculations per second? 1. 65 ns 2. 15 ns 3. 11 ns 4. 67 ns

Answer 107

**2.** 15 ns ## Footnote Here's how I would do it find the time taken in seconds to perform 1 task with the computer working at 6.7 x 107 tasks per second So divide your 1 second by 6.7 x 107 = 14.925 x 10-9 seconds Now find your time in nano seconds Divide the time taken in seconds by the amount of seconds in a nano second, so 14.925 x 10-9 / 1 x 10-9 Gives you 14.925 nano seconds.

Question 108

# Module 01 Exams Albert uses as his unit of length (for walking to visit his neighbors or plowing his fields) the albert (A), the distance Albert can throw a small rock. One albert is How many square alberts is equal to one acre? (1 acre = 43,560 ft² = 4050 m²) 1.

Answer 108

Question 109

# Module 01 Exams When is the average velocity of an object equal to the instantaneous velocity? 1. only when the velocity is increasing at a constant rate 2. never 3. always 4. when the velocity is constant 5. only when the velocity is decreasing at a constant rate

Answer 109

4. when the velocity is constant

Question 110

# Module 01 Exams You drive 6.0 km at 50 km/h and then another 6.0 km at 90 km/h. Your average speed over the 12 km drive will be 1. less than 70 km/h. 2. equal to 70 km/h. 3. greater than 70 km/h. 4. It cannot be determined from the information given because we must also know directions traveled. 5. exactly 38 km/h.

Answer 110

1. less than 70 km/h

Question 111

# Module 01 Exams Suppose that a car traveling to the west begins to slow down as it approaches a traffic light. Which of the following statements about its acceleration is correct? 1. The acceleration is zero. 2. Since the car is slowing down, its acceleration must be negative. 3. The acceleration is toward the east. 4. The acceleration is toward the west.

Answer 111

3. The acceleration is toward the east

Question 112

# Module 01 Exams A ball is thrown straight up, reaches a maximum height, then falls to its initial height. Which of the following statements about the direction of the velocity and acceleration of the ball as it is going up is correct? 1. Both its velocity and its acceleration points downward. 2. Both its velocity and its acceleration point upward. 3. Its velocity points upward and its acceleration points downward. 4. Its velocity points downward and its acceleration points upward.

Answer 112

3. Its velocity points upward and its acceleration points downward

Question 113

# Module 01 Exams Two objects are dropped from a bridge, an interval of 1.0 s apart. Air resistance is negligible. During the time that both objects continue to fall, their separation 1. decreases. 2. increases. 3. decreases at first, but then stays constant. 4. stays constant. 5. increases at first, but then stays constant.

Answer 113

2. increases

Question 114

# Module 01 Exams A child standing on a bridge throws a rock straight down. The rock leaves the child's hand at time t = 0 s. If we take upward as the positive direction, which of the graphs shown below best represents the acceleration of the stone as a function of time?

Answer 114

B.

Question 115

# Module 01 Exams A race car circles 10 times around a circular 8.0-km track in 20 min. Using SI units (a) what is its average speed for the ten laps? (b) what is its average velocity for the ten laps?

Answer 115

(b) The average velocity is equal to zero since the displacement is zero (because the tract is circular so the starting and ending points are the same).

Question 116

# Module 01 Exams Arthur and Betty start walking toward each other when they are 100 m apart. Arthur has a speed of 3.0 m/s and Betty has a speed of 2.0 m/s. How long does it take for them to meet? 1.

Answer 116

Question 117

# Module 01 Exams The position x(t) of a particle as a function of time t is given by the equation x(t) = (3.5 m/s)t - (5.0 m/s2)t2. What is the average velocity of the particle between t = 0.30 s and t = 0.40 s? 1.

Answer 117

Question 118

# Module 01 Exams A package is dropped from a helicopter that is moving upward at 15m/s. If it takes 8s before the package strikes the ground, how high above the ground was the package when it was released? Neglect air resistance. 1.

Answer 118

Question 119

# Module 01 Exams At the same moment, one rock is dropped and one is thrown downward with an initial velocity of 29m/s from the top of a building that is 300m tall. How much earlier does the thrown rock strike the ground? Neglect air resistance. 1.

Answer 119

Question 120

# Module 01 Exams A player kicks a soccer ball in a high arc toward the opponent's goal. At the highest point in its trajectory 1. the ball's acceleration points upward. 2. both the velocity and the acceleration of the soccer ball are zero. 3. neither the ball's velocity nor its acceleration are zero. 4. the ball's acceleration is zero but its velocity is not zero. 5. the ball's velocity points downward.

Answer 120

At the height of the projectile's path, gravity is still an active force on the ball, so there is still acceleration. Furthermore, the Vy component is zero, since the parabola is at its maximum point and changing direction; however, the Vx component is still moving forwards as the ball is thrown. Therefore, the correct answer is (C) that neither the acceleration or velocity is equal to zero.

Question 121

# Module 01 Exams A player throws a football 50.0 m at 61.0° north of west. What is the westward component of the displacement of the football? 1. 0.00 m 2. 24.2 m 3. 64.7m 4. 55.0 m 5. 74.0 m

Answer 121

2. 24.2 m

Question 122

# Module 01 Exams The figure shows three vectors, A, B, and C, along with their magnitudes. Determine the magnitude and direction of the vector given by A - B - C.

Answer 122

Question 123

# Quiz 1.1 Under what condition is average velocity equal to the average of the object's initial and final velocity? 1. This can occur only when the velocity is zero. 2. This can only occur if there is no acceleration. 3. The acceleration must be constantly increasing. 4. The acceleration is constant. 5. The acceleration must be constantly decreasing.

Answer 123

2. This can only occur if there is no acceleration

Question 124

# Quiz 1.1 If, in the figure, you start from the Bakery, travel to the Cafe, and then to the Art Gallery in 2.00 hours, what is your ## Footnote average speed? average velocity?

Answer 124

a. Average Speed: (Distance traveled ÷ time elapsed) = 10.5km/2.00hours=5.25kmh b. Average Velocity: (Displacement ÷ time elapsed) = x2-x1/t2-t1=2.50km-0/km2.00hours=1.25kmh

Question 125

# Quiz 1.1 Suppose that a car traveling to the west (-x direction) begins to slow down as it approaches a traffic light. Which statement concerning its acceleration must be correct? 1. Its acceleration is decreasing in magnitude as the car slows down. 2. Its acceleration is negative. 3. Its acceleration is positive. 4. Its acceleration is zero.

Answer 125

3. Its acceleration is positive.

Question 126

# Quiz 1.1 A racing car accelerates uniformly from rest along a straight track. This track has markers spaced at equal distances along it from the start, as shown in the figure. The car reaches a speed of 140 km/h as it passes marker 2. Where on the track was the car when it was traveling at half this speed, that is at 70 km/h? 1. At marker 1 2. Between marker 1 and marker 2 3. Before marker 1

Answer 126

3. Before marker 1

Question 127

# Quiz 1.1 You drive 6.0 km at 50 km/h and then another 6.0 km at 90 km/h. Your average speed over the 12 km drive will be 1. equal to 70 km/h. 2. exactly 38 km/h. 3. It cannot be determined from the information given because we must also know directions traveled. 4. greater than 70 km/h. 5. less than 70 km/h.

Answer 127

5. less than 70 km/h.

Question 128

# Quiz 1.1 The slope of a velocity versus time graph gives 1. the distance traveled. 2. displacement. 3. velocity. 4. acceleration.

Answer 128

4. acceleration

Question 129

# Quiz 1.1 Consider a deer that runs from point A to point B. The distance the deer runs can be greater than the magnitude of its displacement, but the magnitude of the displacement can never be greater than the distance it runs. True False

Answer 129

True

Question 130

# Quiz 1.2 A soccer ball is released from rest at the top of a grassy incline. After 6.4 seconds the ball has rolled 91 m with constant acceleration, and 1.0 s later it reaches the bottom of the incline. (a) What was the ball's acceleration? (b) How long was the incline?\>

Answer 130

Question 131

# Quiz 1.2 A cart starts from rest and accelerates uniformly at 4.0 m/s2 for 5.0 s. It next maintains the velocity it has reached for 10 s. Then it slows down at a steady rate of 2.0 m/s2 for 4.0 s. What is the final speed of the car? 1. 16 m/s 2. 10 m/s 3. 12 m/s 4. 20 m/s

Answer 131

3. 12 m/s

Question 132

# Quiz 1.2 A car with good tires on a dry road can decelerate (slow down) at a steady rate of about 5.0 m/s2 when braking. If a car is initially traveling at 55 mi/h 1. how much time does it take the car to stop? 2. what is its stopping distance?

Answer 132

Question 133

# Quiz 1.2 An airplane starts from rest and accelerates at a constant 10.8 m/s2. What is its speed at the end of a 400 m-long runway? (show your work)

Answer 133

Question 134

# Quiz 1.2 At the instant a traffic light turns green, a car that has been waiting at the intersection starts ahead with a constant acceleration of 2.00 m/s2. At that moment a truck traveling with a constant velocity of 15.0 m/s overtakes and passes the car. 1. Calculate the time necessary for the car to reach the truck. 2. Calculate the distance beyond the traffic light that the car will pass the truck. 3. Determine the speed of the car when it passes the truck.

Answer 134

Question 135

# Quiz 1.2 Human reaction times are worsened by alcohol. How much further (in feet) would a drunk driver's car travel before he hits the brakes than a sober driver's car? Assume that both are initially traveling at 50.0 mi/h and their cars have the same acceleration while slowing down, and that the sober driver takes 0.33 s to hit the brakes in a crisis, while the drunk driver takes 1.0 s to do so. (5280 ft = 1 mi)

Answer 135

Question 136

# Quiz 1.3 A velocity vector has components 36 m/s westward and 22 m/s northward. What are the magnitude and direction of this vector?

Answer 136

Therefore, the magnitude is 42 m/s in the 31­­° northwest direction.

Question 137

# Quiz 1.3 Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively. If these two vectors are added together, the magnitude of the sum 1. is equal to 2.0 m. 2. is equal to 8.6 m. 3. is equal to 12 m. 4. could be as small as 2.0 m or as large as 12 m.

Answer 137

4. could be as small as 2.0 m or as large as 12 m

Question 138

# Quiz 1.3 If a vector A→ has components Ax \< 0, and Ay \< 0, then the angle that this vector makes with the positive x-axis must be in the range 1. 0° to 90° 2. 90° to 180° 3. 180° to 270° 4. 270° to 360° 5. cannot be determined without additional information

Answer 138

3. 180° to 270°