Q: Alice is skating east at $$3.20 m/s. $$She begins to experience a constant acceleration of $$0.8 m/s$^2$$ westward. What is her velocity after $$3.0 s$$?

$$v = 3.20 - 0.8 \times 3.0 = 0.8 m/s$\;$$ east

Q: The displacement $$\Delta x of an $$object is given by the area under the velocity-time graph. If the velocity is $$4 m/s $$for $$5 s$$, what is the displacement?

$$\Delta x = 4 \times 5 = 20 m$$

Question 1

A student walks along the x-axis, and her position is plotted as a function of time. If the slope of her position-versus-time graph increases, what does this indicate about her motion?

Accepted Answer

She is speeding up.

Question 2

Given the formula for average velocity $$v_{av} = \frac{\Delta x}{\Delta t}$$, what are the SI units for velocity?

Accepted Answer

m/s

Question 3

A skateboarder’s position is tracked and plotted on a position vs. time graph. At $$t = 4 s$$, the position is $$x = 0 m$$, and at $$t = 8 s$$, the position is $$x = 10 m. $$What is the average velocity between $$t = 4 s $$and $$t = 8 s$$?

Accepted Answer

$$2.5 m/s$$

Question 4

Which of the following statements is true about the area under a velocity-versus-time graph?

Accepted Answer

It represents the object's displacement.

Question 5

Bob’s position as a function of time is plotted on a graph. At which points is Bob at rest?

Accepted Answer

Where the graph is a horizontal line.

Question 6

A lion accelerates from rest at $$a = 9.5 m/s$^2 to a $$speed of $$v = 4.5 m/s. $$How much time does this take?

Accepted Answer

$$t = \frac{v}{a} = \frac{4.5}{9.5} = 0.47 s$$

Question 7

If an object’s velocity is negative and its acceleration is positive, what is happening to the object?

Accepted Answer

It is slowing down.

Question 8

A car moves along a straight road. Its velocity-versus-time graph is a horizontal line at $$v = 3 m/s. $$What does this indicate about the car’s motion?

Accepted Answer

The car is moving at constant velocity.

Question 9

Alice is skating east at $$3.20 m/s. $$She begins to experience a constant acceleration of $$0.8 m/s$^2$$ westward. What is her velocity after $$3.0 s$$?

Accepted Answer

$$v = 3.20 - 0.8 	imes 3.0 = 0.8 m/s$\;$$ east

Question 10

Which of the following best describes instantaneous velocity?

Accepted Answer

The velocity at a specific instant of time.

Question 11

A velocity-versus-time graph for an object is a straight line with a positive slope. What does this indicate?

Accepted Answer

The object is accelerating at a constant rate.

Question 12

If the position-versus-time graph of an object is a curve, what does this tell you about the object’s velocity?

Accepted Answer

The velocity is changing.

Question 13

A runner moves from $$x_i = -2 m to$$ $$x_f = 6 m in$$ $$t = 4 s. $$What is the runner’s average velocity?

Accepted Answer

$$v_{av} = \frac{6 - (-2)}{4} = 2 m/s$$

Question 14

Which of the following is a correct interpretation of a negative velocity in one-dimensional motion?

Accepted Answer

The object is moving in the negative direction.

Question 15

The displacement $$\Delta x of an $$object is given by the area under the velocity-time graph. If the velocity is $$4 m/s $$for $$5 s$$, what is the displacement?

Accepted Answer

$$\Delta x = 4 	imes 5 = 20 m$$

Question 16

A student’s position-versus-time graph is a straight line with a negative slope. What does this indicate about the student’s motion?

Accepted Answer

The student is moving in the negative direction at constant speed.

Question 17

If an object starts at the origin and its velocity is given by $$v(t) = 4 m/s $$for $$t \u003c 4 s $$and $$v(t) = 0$$ for $$t \geq 4 s$$, what is its position at $$t = 4 s$$?

Accepted Answer

$$x = 16 m$$

Question 18

Which of the following best describes the difference between displacement and distance traveled?

Accepted Answer

Displacement is the straight-line change in position; distance is the total path length.

Question 19

A car’s velocity changes from $$10 m/s to$$ $$-5 m/s in$$ $$3 s. $$What is the average acceleration?

Accepted Answer

$$a_{av} = \frac{-5 - 10}{3} = -5 m/s$^2$$

Representing Motion: Position, Velocity, and Acceleration in One Dimension

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