Question 1

Which of the following best describes the meaning of the slope of a position vs. time graph?

Accepted Answer

It represents the object's velocity at that instant.

Question 2

A car moves along a straight road such that its position as a function of time is given by $$x(t) = 4t^2$ - 2t. $$What is the car's instantaneous velocity at $$t = 3 s$$?

Accepted Answer

$$v = 22 m/s$$

Question 3

If the velocity of an object is constant and positive, which of the following statements about its position vs. time graph is correct?

Accepted Answer

The graph is a straight line with a positive slope.

Question 4

Given the position function $$x(t) = -t^2$ + 3t$$, what is the velocity at $$t = 2 s$$?

Accepted Answer

$$v = -9 m/s$$

Question 5

A runner moves with a constant velocity of $$5 m/s $$for $$8$$ seconds. If the initial position is $$x_i = 0 m$$, what is the final position?

Accepted Answer

$$x_f = 40 m$$

Question 6

Which of the following is the correct formula for average velocity over a time interval?

Accepted Answer

$$v_{avg} = \frac{\Delta x}{\Delta t}$$

Question 7

A cyclist starts at $$x = 0 m $$and moves east at $$12 m/s. $$After $$15$$ seconds, what is the cyclist's position?

Accepted Answer

$$x = 180 m$$

Question 8

If the position vs. time graph of an object is a horizontal line, what can you conclude about the object's motion?

Accepted Answer

The object is at rest.

Question 9

Suppose two cars start at different locations and drive towards each other. Car A starts at $$x = 0$$ and drives east at $$60$$ mph. Car B starts $$400$$ miles east and drives west at $$40$$ mph. How long after Car A starts will they meet?

Accepted Answer

$$4$$ hours

Question 10

Which of the following statements about the derivative of a constant is correct?

Accepted Answer

$$\frac{d}{dt}(c) = 0$$

Question 11

The area under a velocity vs. time graph between $$t_1$$ and $$t_2$$ represents:

Accepted Answer

The object's displacement during that time interval.

Question 12

If the position of a particle is given by $$x(t) = 5t^3$, what is its velocity at t = 2$ s?

Accepted Answer

$$v = 60 m/s$$

Question 13

A position vs. time graph has a steep negative slope. What does this indicate about the object's motion?

Accepted Answer

The object is moving quickly in the negative direction.

Question 14

Which of the following is the correct rule for the derivative of a sum of two functions $$u(t)$$ and $$w(t)$$?

Accepted Answer

$$\frac{d}{dt}(u+w) = \frac{du}{dt} + \frac{dw}{dt}$$

Question 15

A position graph shows a curve that becomes steeper over time. What does this indicate about the object's velocity?

Accepted Answer

The object's velocity is increasing.

Question 16

If $$x(t) = 7t^2$ + 2t$$, what is the velocity function $$v(t)$$?

Accepted Answer

$$v(t) = 14t + 2$$

Question 17

A position vs. time graph for a moving elevator shows a tangent with zero slope at $$t = 5 s. $$What does this mean about the elevator's velocity at that instant?

Accepted Answer

The elevator's velocity is zero.

Question 18

Which of the following is a correct interpretation of the equation $$x_f = x_i + v_x \Delta t$$ for uniform motion?

Accepted Answer

Final position equals initial position plus velocity times time interval.

Question 19

A position graph shows a straight line with a negative slope. What does this tell you about the object's motion?

Accepted Answer

The object is moving with constant negative velocity.

Kinematics: Position, Velocity, and Calculus in Motion

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