Q: A runner moves with a velocity of $$3.0\ \mathrm{m/s}$$ for $$4.0\ \mathrm{s}$$, then $$-2.0\ \mathrm{m/s}$$ for $$2.0\ \mathrm{s}. $$What is the runner’s net displacement?

$$(3.0 \times 4.0) + (-2.0 \times 2.0) = 12.0 - 4.0 = 8.0\ \mathrm{m}$$

Q: Alice is skating east at $$3.20\ \mathrm{m/s}$$ and begins to experience a constant acceleration of $$0.8\ \mathrm{m/s^2$}$$ west. What is her velocity after $$3.0\ \mathrm{s}$$?

$$v = 3.20 + (-0.8) \times 3.0 = 0.8\ \mathrm{m/s}$$

Question 1

A student walks along the x-axis, and her position is described by $$x(t) = 2t + 3 ($$where $$x is in $$meters and $$t in $$seconds). What is her velocity?

Accepted Answer

$$2\ \mathrm{m/s}$$

Question 2

Which of the following best describes the meaning of a negative velocity in one-dimensional motion?

Accepted Answer

The object is moving in the direction opposite to the defined positive axis.

Question 3

A car moves along a straight road. Its position-versus-time graph is a straight line with a positive slope. What does this indicate about the car's motion?

Accepted Answer

The car is moving at a constant positive velocity.

Question 4

Given the velocity-time graph of an object, how can you determine the object's displacement over a time interval?

Accepted Answer

By calculating the area under the velocity-time graph during the interval.

Question 5

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

Accepted Answer

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

Question 6

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

Accepted Answer

The velocity is changing (not constant).

Question 7

A skateboarder’s position is tracked and plotted as a straight line with a negative slope on a position vs. time graph. What is the skateboarder’s velocity?

Accepted Answer

Constant and negative

Question 8

Bob’s position as a function of time is shown in a graph. At which times is Bob at rest?

Accepted Answer

When the position vs. time graph is flat (horizontal)

Question 9

A runner moves with a velocity of $$3.0\ \mathrm{m/s}$$ for $$4.0\ \mathrm{s}$$, then $$-2.0\ \mathrm{m/s}$$ for $$2.0\ \mathrm{s}. $$What is the runner’s net displacement?

Accepted Answer

$$(3.0 	imes 4.0) + (-2.0 	imes 2.0) = 12.0 - 4.0 = 8.0\ \mathrm{m}$$

Question 10

Which of the following statements about average velocity is correct?

Accepted Answer

Average velocity is a vector defined as $$\vec{v}_{av} = \frac{\Delta \vec{x}}{\Delta t}$$

Question 11

A car’s velocity changes from $$10\ \mathrm{m/s} to$$ $$-5\ \mathrm{m/s} in$$ $$3\ \mathrm{s}. $$What is its average acceleration?

Accepted Answer

$$a_{av} = \frac{-5 - 10}{3} = \frac{-15}{3} = -5\ \mathrm{m/s^2$}$$

Question 12

If the area under a velocity-time graph from $$t=0 to$$ $$t=4 s is$$ $$16\ \mathrm{m}$$, what is the object’s displacement?

Accepted Answer

$$16\ \mathrm{m}$$

Question 13

Alice is skating east at $$3.20\ \mathrm{m/s}$$ and begins to experience a constant acceleration of $$0.8\ \mathrm{m/s^2$}$$ west. What is her velocity after $$3.0\ \mathrm{s}$$?

Accepted Answer

$$v = 3.20 + (-0.8) 	imes 3.0 = 0.8\ \mathrm{m/s}$$

Question 14

Which of the following is true about instantaneous velocity?

Accepted Answer

It is the slope of the tangent to the position vs. time graph at a specific instant.

Question 15

A position vs. time graph is a horizontal line. What does this indicate about the object’s motion?

Accepted Answer

The object is at rest.

Question 16

A car’s velocity-time graph is a horizontal line at $$v = 5\ \mathrm{m/s}. $$What is the car’s acceleration?

Accepted Answer

$$0\ \mathrm{m/s^2$}$$

Question 17

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 traveled.

Question 18

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

Accepted Answer

It is slowing down.

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

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