3A1 Motion

Question 1

Fill in the blank:

Motion is the act of changing the _______ or orientation.

Answer 1

position

Motion requires both displacement and time to define changes.

Question 2

Define:

Kinematics

Answer 2

The study of motion without reference to the forces that cause it.

Kinematics focuses on characteristics associated with the motion of objects.

Question 3

Define:

Scalar quantity

Answer 3

Physical quantity described only by its magnitude.

Example: The height of a building can be described as 80 feet.

Question 4

Define:

Vector quantity

Answer 4

Physical quantity with a magnitude and a direction.

Magnitude is similar to absolute value, and direction is often defined by the context of the problem.

Question 5

Why are scalar and vector quantities both essential in describing motion?

Answer 5

Scalar quantities provide information on the magnitude, while vector quantities describe both magnitude and direction. Together, they give a complete picture of motion.

Scalar and vector quantities work together to fully define motion, with scalars describing how much, and vectors describing in which direction.

Question 6

Explain how a vector quantity is represented graphically.

Answer 6

A vector is graphically represented by an arrow; its length indicates magnitude, and its direction indicates the vector’s orientation.

Examples include velocity and force.

Question 7

True or False:

Distance and displacement always have the same magnitude.

Answer 7

False

Distance is the total path traveled, while displacement is the shortest path between two points.

Question 8

Fill in the blank:

Velocity is a vector quantity calculated by taking the change in position and dividing by the change in _____.

Answer 8

time

The SI unit of velocity is m/s.

Question 9

What is the primary difference between velocity and speed?

Answer 9

• Velocity is a vector quantity with magnitude and direction.
• Speed is scalar and has only magnitude.

Velocity can be negative based on direction, unlike speed.

Question 10

Fill in the blank:

Energy is a scalar quantity because it has only ______ and no direction.

Answer 10

magnitude

Energy is defined by its amount, not by its orientation.

Question 11

True or False:

Time can be considered a vector quantity in specific scenarios.

Answer 11

False

Time has no direction and is measured only as a magnitude.

Question 12

True or False:

Scalars can be added directly, while vectors require the use of component-wise addition.

Answer 12

True

Scalars add algebraically, while vector addition involves summing corresponding components.

Question 13

How can vectors be represented in mathematics?

Answer 13

Vectors can be represented using:

• Bold letters (e.g., x, y, z)
• Letters with a right-facing arrow
• Angle brackets (e.g., <x, y>)

Using angle brackets is a common method in written work.

Question 14

Fill in the blank:

The _______ of a vector is represented by the angle it forms with a reference axis.

Answer 14

direction

The direction of a vector is typically given by the angle relative to the positive x-axis in a 2D system.

Question 15

Fill in the blank:

The magnitude of a vector can be calculated using the _______ formula when its components are known.

Answer 15

pythagorean

The magnitude of a vector equation, ||v|| = √(x² + y²), was derived from the Pythagorean theorem.

Question 16

Define:

Vector components

Answer 16

Projections of a vector onto the coordinate axes (e.g., v_x and v_y). They simplify vector calculations like addition, subtraction, and resolving forces.

Components allow complex vectors to be analyzed using simple algebra and trigonometry.

Question 17

Define:

Position

Answer 17

The location of an object within a specified frame of reference.

Position is a scalar quantity.

Question 18

What does velocity describe?

Answer 18

How fast and in which direction an object is moving.

Velocity is a vector quantity.

Question 19

Fill in the blank:

The rate of change of velocity with respect to time is known as _______.

Answer 19

acceleration

Acceleration is a vector quantity that can describe an increase or decrease in velocity and includes the direction of the change.

Question 20

Explain how force is related to acceleration.

Answer 20

Force is directly proportional to acceleration, as stated in Newton’s Second Law of Motion: Force (F) = mass (m) × acceleration (a).

Force is a vector quantity, and its direction matches the direction of acceleration.

Question 21

What is the significance of momentum, and how is it calculated?

Answer 21

Momentum is a vector quantity representing the product of an object’s mass and velocity. It is calculated as: Momentum (p) = mass (m) × velocity (v).

Momentum indicates how difficult it is to stop a moving object and depends on both its speed and direction.

Question 22

Define:

Linear motion

Answer 22

Motion along any line, also called 1-D motion.

Linear motion is the simplest form of motion and involves scalar and vector quantities like speed and velocity. It can be a straight line or a curved line.

Question 23

Why is it important to consider reference frames in describing motion?

Answer 23

These frames determine how motion is observed and measured, affecting velocity and displacement.

Motion is relative and depends on the observer’s point of view.

Question 24

Fill in the blank:

The formula for final velocity at constant acceleration, in rectilinear motion is given by the equation: v = v₀ + at , where v₀ represents ________ ________.

Answer 24

initial velocity

This equation is part of the kinematic formulas used in linear motion.

Question 25

Explain the *difference* between **uniform** and **non-uniform** motion in a straight line.

Answer 25

* Uniform motion occurs when an object moves with **constant velocity**. * Non-uniform motion involves **changing velocity**. ## Footnote Non-uniform motion is characterized by acceleration or deceleration.

Question 26

What is the equation for **exact position of the object** in linear motion with constant acceleration?

Answer 26

s = ut + ½at² ## Footnote This formula combines initial velocity (u), acceleration (a), and time (t) to calculate exact position (s).

Question 27

A car accelerates uniformly from rest at 2m/s². **How far** does it travel in **5s**?

Answer 27

The distance (s) is calculated using the formula: s = (1/2)at² s = (1/2)(2m/s²)(5s)² s =25m ## Footnote Uniform acceleration equations describe linear motion.

Question 28

# Define: Projectile motion

Answer 28

It describes the **curved path** an object follows when launched into the air, under the influence of gravity alone. ## Footnote The motion has both horizontal and vertical components.

Question 29

# Fill in the blanks: The **horizontal** motion of a projectile has constant \_\_\_\_\_\_, while its **vertical** motion is affected by \_\_\_\_\_\_.

Answer 29

velocity, gravity ## Footnote Horizontal and vertical motions are independent of each other.

Question 30

What is the **trajectory** of a projectile?

Answer 30

The trajectory is a **parabolic path**. ## Footnote The shape is due to constant horizontal velocity and uniformly accelerated vertical motion.

Question 31

What two factors determine the **range of a projectile**?

Answer 31

* Initial velocity * Angle of launch ## Footnote The optimal launch angle for maximum range is 45°.

Question 32

Explain why the **vertical velocity** of a projectile **changes** over time.

Answer 32

**Gravity** causes a uniform acceleration of -9.8 m/s², altering the vertical velocity. ## Footnote At the peak, the vertical velocity is zero.

Question 33

What is the significance of the **time of flight** in projectile motion?

Answer 33

It represents the **total time** the projectile spends in the air. ## Footnote Time of flight depends on the initial vertical velocity and the height of the launch.

Question 34

# Fill in the blank: The **horizontal acceleration** of a projectile is \_\_\_\_\_.

Answer 34

zero ## Footnote In ideal conditions without air resistance, horizontal acceleration is zero.

Question 35

What happens to the **vertical displacement** of a **projectile** after reaching its peak?

Answer 35

It **decreases** as the projectile falls back to the ground. ## Footnote This is due to the **downward acceleration** of gravity.

Question 36

What does the **slope of a velocity-time graph** represent in linear motion?

Answer 36

It represents **acceleration**. ## Footnote A positive slope indicates increasing velocity, while a negative slope shows deceleration.

Question 37

# True or False: The **distance** traveled in a straight line can be calculated using the **area under a velocity-time graph**.

Answer 37

True ## Footnote The area under the graph equals displacement in cases where direction is considered.

Question 38

# True or False: The **slope** of a position-time graph represents **velocity**.

Answer 38

True ## Footnote A steeper slope indicates a higher velocity, while a horizontal line represents zero velocity.

Question 39

What does a **curved line** on a **position-time graph** indicate?

Answer 39

It indicates **changing velocity**, or accelerated motion. ## Footnote The curvature shows how the rate of change of position is increasing or decreasing.

Question 40

# True or false: The **area** under an acceleration-time graph represents **velocity**.

Answer 40

True ## Footnote This is based on the relationship a= Δv/Δt

Question 41

What does a **horizontal line** on a **velocity-time graph** indicate?

Answer 41

It indicates **constant velocity**. ## Footnote In this case, acceleration is zero.

Question 42

# Fill in the blank: On a position-time graph, if the **slope is negative** the motion is \_\_\_\_\_\_.

Answer 42

backwards ## Footnote A negative slope means the position is decreasing over time.

Question 43

What does the **intersection** of two lines on a **position-time graph** indicate?

Answer 43

It indicates that two objects have the **same position** at that moment. ## Footnote This could mean the objects meet or cross paths.

Question 44

# Define: Circular motion

Answer 44

Movement of an object along a **circular path**, such as a satellite orbiting Earth. ## Footnote The motion involves centripetal force and acceleration.

Question 45

# Fill in the blank: The **acceleration** directed toward the center of a circle in **circular motion** is called \_\_\_\_\_\_ \_\_\_\_\_\_.

Answer 45

centripetal acceleration ## Footnote It is given by ac=v²/r, where v is velocity and r is radius.

Question 46

What does **centripetal force** depend on?

Answer 46

It depends on: * velocity * radius of the circle ## Footnote Centripetal force keeps the object in circular motion.

Question 47

# True or false: An object in **uniform** circular motion has a **constant velocity**.

Answer 47

False ## Footnote While the speed is constant, the velocity **changes due to direction**.

Question 48

How is **angular velocity** related to circular motion?

Answer 48

It measures **how fast an object rotates** around a central point, typically in radians per second. ## Footnote It is related to linear velocity by v=rω.

Question 49

# Define: Simple harmonic motion (SHM)

Answer 49

A type of **periodic motion where an object oscillates back and forth** around a fixed equilibrium point. ## Footnote The acceleration is always proportional to its displacement from that point and directed opposite to the displacement.

Question 50

# Fill in the blank: In **Simple harmonic motion**, the time it takes to complete one **full cycle** is called the \_\_\_\_\_\_.

Answer 50

period ## Footnote The period is inversely related to frequency.

Question 51

What is the formula for the **period** of a simple pendulum?

Answer 51

T=2π√(L/g) ## Footnote Where L is length and g is gravitational acceleration. The period depends on the length of the pendulum and gravity.

Question 52

What is the **amplitude** in SHM?

Answer 52

It is the **maximum displacement** from the equilibrium position. ## Footnote It determines the energy of the motion.

Question 53

Explain how **energy** transforms in SHM.

Answer 53

Energy alternates between **kinetic** and **potential** forms in SHM. ## Footnote At maximum displacement, energy is all potential; at equilibrium, it is all kinetic.

Question 54

# True or false: In SHM, the **acceleration** of an object is always directed towards the **equilibrium position**.

Answer 54

True ## Footnote The acceleration in SHM is proportional to the displacement from the equilibrium position and always acts to restore equilibrium.

Question 55

# Fill in the blanks: The **time period** of a **mass-spring system** in SHM depends on \_\_\_\_\_ and \_\_\_\_\_.

Answer 55

the mass (m); the spring constant (k) ## Footnote This relationship shows that SHM frequency increases with a stiffer spring and decreases with higher mass.

Question 56

What is the relationship between the **frequency** and **period** of an SHM system?

Answer 56

The frequency (f) is the **reciprocal** of the period (T), given by **f=1/T**. ## Footnote Frequency represents the number of oscillations per second, while the period is the time taken for one complete oscillation.

Question 57

How does the **angular frequency** (ω) relate to the time **period** (T) in SHM?

Answer 57

Angular frequency is **inversely proportional** to time period given by ω=2π/T. ## Footnote Angular frequency is often used to describe oscillatory systems and is measured in radians per second.

Question 58

# True or false: The **restoring force** in SHM is **independent of displacement**.

Answer 58

False ## Footnote In SHM, the restoring force is directly proportional to displacement and follows Hooke’s Law: F=−kx.

Question 59

A mass on a spring oscillates with an **amplitude of 0.5m** and a **period of 2s**. What is the **angular frequency**?

Answer 59

Using ω=2π/T: **ω**=2π/2=**πrad/s** ## Footnote Angular frequency is a key parameter in SHM.