1.5 The Kinematics Equations

Question 1

What is the formula for the area of a trapezoid?

Answer 1

A = (b1 + b2) / 2 * h

b1 and b2 are the lengths of the parallel sides, and h is the height.

Question 2

How do you calculate displacement from a velocity-time graph?

Answer 2

Use the area under the curve of the graph

Displacement can be calculated as the area between the velocity curve and the time axis.

Question 3

What is the equation derived from the area under the velocity-time graph?

Answer 3

d = Vave * At

d represents displacement, Vave is average velocity, and At is the time interval.

Question 4

What does the variable ‘At’ represent in the equation d = Vave * At?

Answer 4

At represents the time interval

It is the duration over which the average velocity is calculated.

Question 5

In the context of a velocity-time graph, what does the area under the graph represent?

Answer 5

Displacement

The area can be calculated using geometric methods depending on the shape under the curve.

Question 6

True or False: The area under a velocity-time graph can be used to determine distance traveled.

Answer 6

True

Distance is the total displacement, considering the direction of motion.

Question 7

What does the area under the velocity-time graph represent?

Answer 7

The equation d = Vave At

This equation is derived from the area under the velocity-time graph.

Question 8

What is the second kinematics equation?

Answer 8

Ad = (V_i + V_f) At

In this equation, V_i is the initial velocity, V_f is the final velocity, and At is the time interval.

Question 9

In the equation Ad = (V_i + V_f) At, what does At represent?

Answer 9

The time interval

At is the duration over which the velocities are averaged.

Question 10

Fill in the blank: The second kinematics equation is Ad = _______.

Answer 10

(V_i + V_f) At

Question 11

What does the area under the velocity-time graph represent?

Answer 11

The equation d = Vave At

This equation is derived from the area under the velocity-time graph.

Question 12

What is the second kinematics equation?

Answer 12

Ad = (V_i + V_f) At

In this equation, V_i is the initial velocity, V_f is the final velocity, and At is the time interval.

Question 13

In the equation Ad = (V_i + V_f) At, what does At represent?

Answer 13

The time interval

At is the duration over which the velocities are averaged.

Question 14

Fill in the blank: The second kinematics equation is Ad = _______.

Answer 14

(V_i + V_f) At

Question 15

How can you calculate the area under a velocity-time graph?

Answer 15

By considering it as a combination of a triangle and a rectangle.

Question 16

What does the area of the rectangle under a velocity-time graph represent?

Answer 16

The displacement of an object traveling with a constant velocity.

Question 17

What is the formula for the area of the rectangle in a velocity-time graph?

Answer 17

Area = V * Δt

Question 18

What does the height of the rectangle represent in a velocity-time graph?

Answer 18

The constant velocity, V.

Question 19

What does the base of the rectangle represent in a velocity-time graph?

Answer 19

The time interval, Δt.

Question 20

What does the area of the triangle under a velocity-time graph represent?

Answer 20

The additional displacement resulting from the change in velocity.

Question 21

What is the height of the triangle in a velocity-time graph?

Answer 21

ΔV = V - V₀

Question 22

What is the base of the triangle in a velocity-time graph?

Answer 22

Δt.

Question 23

What is the formula for the area of the triangle in a velocity-time graph?

Answer 23

Area = 0.5 * base * height

Question 24

What is the final displacement formula combining both areas under the velocity-time graph?

Answer 24

Ad = V * Δt + 0.5 * ΔV * Δt.

Question 25

Who achieved the fastest time of covering 1.6 km while flipping tiddly winks?

Answer 25

E. Wynn and Culliongham (UK).

Question 26

What was the time taken to cover 1.6 km by E. Wynn and Culliongham?

Answer 26

52 minutes and 10 seconds.

Question 27

What was the speed of E. Wynn and Culliongham during their record?

Answer 27

1.8 km/h.

Question 28

True or False: The area under a velocity-time graph can only be a rectangle.

Answer 28

False.

Question 29

Fill in the blank: The area of the triangle can be calculated as _______.

Answer 29

0.5 * Δt * ΔV.

Question 30

What is the first step to obtain the fourth kinematics equation?

Answer 30

Derive the value of a required variable in one equation

Question 31

After isolating V in the equation, what do you substitute it with?

Answer 31

Substitute v - GAt for v

Question 32

What is the second equation used in the derivation process?

Answer 32

Ad = (V + v)At

Question 33

What does the equation Ad = (V + v)At become after substitution?

Answer 33

Ad = (T - GAt + T)At

Question 34

What is the result of simplifying the equation Ad = (T - GAt + T)At?

Answer 34

Ad = 2

Question 35

Fill in the blank: To derive the fourth kinematics equation, you must _______.

Answer 35

[simplify the substituted equation]

Question 36

Is the equation Ad = (V + v)At used in the process of obtaining the fourth kinematics equation?

Answer 36

True

Question 37

What mathematical technique is used to derive the fifth kinematics equation?

Answer 37

Difference of squares ## Footnote The difference of squares is expressed as (a + b)(a - b) = a² - b².

Question 38

What is the isolated form of At in the equation a = ?

Answer 38

At = ? ## Footnote The specific equation for acceleration (a) was not provided in the text.

Question 39

What is the scalar form of the equation used for dividing vectors?

Answer 39

Ad = (v + v)At ## Footnote This represents the scalar form of the kinematics equation.

Question 40

How far did the tortoise cover at the National Tortoise Championships?

Answer 40

5.48 m ## Footnote The tortoise set a world record on July 2, 1977.

Question 41

What was the speed of the tortoise in km/h?

Answer 41

0.45 km/h ## Footnote This speed was recorded during the championships.

Question 42

What is the more standard form of the fifth kinematics equation?

Answer 42

v = y + 2aAd ## Footnote This equation relates velocity, displacement, and acceleration.

Question 43

Fill in the blank: The fifth kinematics equation involves the difference of ______.

Answer 43

squares ## Footnote This refers to the mathematical technique used in deriving the equation.

Question 44

What mathematical technique is used to derive the fifth kinematics equation?

Answer 44

Difference of squares ## Footnote The difference of squares is expressed as (a + b)(a - b) = a² - b².

Question 45

What is the isolated form of At in the equation a = ?

Answer 45

At = ? ## Footnote The specific equation for acceleration (a) was not provided in the text.

Question 46

What is the scalar form of the equation used for dividing vectors?

Answer 46

Ad = (v + v)At ## Footnote This represents the scalar form of the kinematics equation.

Question 47

How far did the tortoise cover at the National Tortoise Championships?

Answer 47

5.48 m ## Footnote The tortoise set a world record on July 2, 1977.

Question 48

What was the speed of the tortoise in km/h?

Answer 48

0.45 km/h ## Footnote This speed was recorded during the championships.

Question 49

What is the more standard form of the fifth kinematics equation?

Answer 49

v = y + 2aAd ## Footnote This equation relates velocity, displacement, and acceleration.

Question 50

Fill in the blank: The fifth kinematics equation involves the difference of ______.

Answer 50

squares ## Footnote This refers to the mathematical technique used in deriving the equation.