Q: A cheetah chases a gazelle across the savannah, as shown in the image. If the cheetah starts at position $$x_0 = 0$ m and reaches the gazelle at x = 80$ m in t = 4$ s, what is the cheetah's average velocity during the chase?

$$v_{avg} = \frac{80\ \text{m}}{4\ \text{s}} = 20\ \text{m/s}$$

Q: A runner moves along a straight track. At $$t = 0 s$$, she is at $$x = 0 m. At$$ $$t = 4 s$$, she is at $$x = -20 m. $$What is her average velocity?

$$v_{avg} = \frac{-20\ \text{m}}{4\ \text{s}} = -5\ \text{m/s}$$

Question 1

A cheetah chases a gazelle across the savannah, as shown in the image. If the cheetah starts at position $$x_0 = 0$ m and reaches the gazelle at x = 80$ m in t = 4$ s, what is the cheetah's average velocity during the chase?

Accepted Answer

$$v_{avg} = \frac{80\ 	ext{m}}{4\ 	ext{s}} = 20\ 	ext{m/s}$$

Question 2

In the motion map with cars labeled A–F, which car has the greatest instantaneous velocity at the moment shown?

Accepted Answer

Car C, because the spacing between its positions is the largest.

Question 3

Given the position vs. time graph for a car, what feature of the graph tells you the car's instantaneous velocity at $$t = 3 s$$?

Accepted Answer

The slope of the tangent to the curve at $$t = 3 s.$$

Question 4

A car moves from $$x = 10 m at$$ $$t = 2 s to$$ $$x = 40 m at$$ $$t = 5 s. $$What is its displacement and average velocity during this interval?

Accepted Answer

Displacement: $$\Delta x = 30 m$$, Average velocity: $$v_{avg} = 10 m/s$$

Question 5

Which of the following best describes the difference between position and displacement?

Accepted Answer

Position is the location at a specific time, while displacement is the change in position over a time interval.

Question 6

A runner moves along a straight track. At $$t = 0 s$$, she is at $$x = 0 m. At$$ $$t = 4 s$$, she is at $$x = -20 m. $$What is her average velocity?

Accepted Answer

$$v_{avg} = \frac{-20\ 	ext{m}}{4\ 	ext{s}} = -5\ 	ext{m/s}$$

Question 7

If the slope of a position vs. time graph is negative, what does this indicate about the object's motion?

Accepted Answer

The object is moving in the negative direction.

Question 8

A car travels 100 m east in 5 s, then 60 m west in 3 s. What is the car's total displacement and average velocity for the entire trip?

Accepted Answer

Displacement: $$40 m $$east, Average velocity: $$v_{avg} = \frac{40\ 	ext{m}}{8\ 	ext{s}} = 5\ 	ext{m/s}$$ east

Question 9

Which of the following statements about velocity is correct?

Accepted Answer

Velocity is a vector quantity; its sign indicates direction.

Question 10

A car's position is given by $$x(t) = 2t^2$ + 3t. $$What is the instantaneous velocity at $$t = 2 s$$?

Accepted Answer

$$v(2) = \frac{d}{dt}(2t^2$ + 3t) = 4t + 3 = 11 m/s$$

Question 11

On a position vs. time graph, what does a horizontal line represent?

Accepted Answer

The object is at rest.

Question 12

A cyclist moves with a constant velocity of $$v = 5 m/s $$for 10 s. What is the total displacement?

Accepted Answer

$$\Delta x = v \Delta t = 5 	imes 10 = 50 m$$

Question 13

If an object's velocity changes from $$+10 m/s to$$ $$-5 m/s$$, what can you say about its motion?

Accepted Answer

The object has reversed direction.

Question 14

A car starts at $$x = 0 m $$and moves with a velocity described by $$v(t) = 4 m/s $$for 5 s, then $$v(t) = -2 m/s $$for 3 s. What is its final position?

Accepted Answer

$$x_f = (4 	imes 5) + (-2 	imes 3) = 20 - 6 = 14 m$$

Question 15

Which of the following best describes instantaneous velocity?

Accepted Answer

The rate at which an object's position is changing at a particular instant.

Question 16

A car moves with a velocity that changes from $$2 m/s to$$ $$6 m/s $$over $$2 s. $$What is the average velocity during this interval?

Accepted Answer

$$v_{avg} = \frac{2 + 6}{2} = 4 m/s$$

Question 17

In a predator-prey chase, the prey runs in a straight line with constant velocity. The predator starts from rest and accelerates uniformly. Which graph best represents the predator's position vs. time?

Accepted Answer

A curve that gets steeper with time (parabolic).

Motion in One Dimension: Position, Displacement, and Velocity

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