Q: A sprinter runs $$1.00 \times 10^2$ m in 10.0 s, then jogs back 1.50$$ \times $$10^2 m in 40.0 s. $$What is her average speed for the total trip?

$$\text{Average speed} = \frac{2.50 \times 10^2$ \text{ m}}{50.0 \text{ s}} = 5.00 m/s$$

Q: What is the average velocity of the sprinter in the previous question?

$$v_{avg} = \frac{-5.0 \times 10^1$ \text{ m}}{50.0 \text{ s}} = -1.0 m/s$$

Q: A car accelerates from rest to $$27.8 m/s in$$ $$2.6 s. $$What is its average acceleration?

$$a_{avg} = \frac{27.8 \text{ m/s} - 0}{2.6 \text{ s}} = 10.7 m/s$^2$$

Q: If the position of a particle as a function of time is given by $$x(t) = 4t^2$ - 2t + 1$$, what is the instantaneous velocity at $$t = 3 s$$?

$$v = \frac{dx}{dt} = 8t - 2;\ v(3) = 8 \times 3 - 2 = 22 m/s$$

Question 1

A person walks from $$x_i = 2 m to$$ $$x_f = 7 m $$along a straight path. What is the displacement of the person?

Accepted Answer

$$\Delta x = 5 m$$

Question 2

A runner starts at the origin and runs 4.3 miles to the grocery store, then returns home. What is the total distance traveled and the displacement?

Accepted Answer

Distance = 8.6 mi, Displacement = 0 mi

Question 3

Which of the following statements about displacement and distance is correct?

Accepted Answer

Displacement can be negative, but distance is always positive.

Question 4

Given the position-time data: $$t = 0 s$$, $$x = 1 m$$; $$t = 1 s$$, $$x = 3 m$$; $$t = 2 s$$, $$x = 4 m$$; $$t = 3 s$$, $$x = 2 m$$; $$t = 4 s$$, $$x = -1 m. $$What is the average velocity between $$t = 1 s $$and $$t = 4 s$$?

Accepted Answer

$$v_{avg} = \frac{-1 - 3}{4 - 1} = -1.33 m/s$$

Question 5

A sprinter runs $$1.00 	imes 10^2$ m in 10.0 s, then jogs back 1.50$$ 	imes $$10^2 m in 40.0 s. $$What is her average speed for the total trip?

Accepted Answer

$$	ext{Average speed} = \frac{2.50 	imes 10^2$ 	ext{ m}}{50.0 	ext{ s}} = 5.00 m/s$$

Question 6

What is the average velocity of the sprinter in the previous question?

Accepted Answer

$$v_{avg} = \frac{-5.0 	imes 10^1$ 	ext{ m}}{50.0 	ext{ s}} = -1.0 m/s$$

Question 7

Which of the following best describes instantaneous velocity?

Accepted Answer

The slope of the tangent line to the position vs. time graph at a given point.

Question 8

A car accelerates from rest to $$27.8 m/s in$$ $$2.6 s. $$What is its average acceleration?

Accepted Answer

$$a_{avg} = \frac{27.8 	ext{ m/s} - 0}{2.6 	ext{ s}} = 10.7 m/s$^2$$

Question 9

Which of the following is true about average speed and average velocity?

Accepted Answer

Average speed is always positive, but average velocity can be negative.

Question 10

If the position of a particle as a function of time is given by $$x(t) = 4t^2$ - 2t + 1$$, what is the instantaneous velocity at $$t = 3 s$$?

Accepted Answer

$$v = \frac{dx}{dt} = 8t - 2;\ v(3) = 8 	imes 3 - 2 = 22 m/s$$

Question 11

A particle moves along the x-axis such that its velocity changes from $$5 m/s to$$ $$-3 m/s in$$ $$4$$ seconds. What is its average acceleration?

Accepted Answer

$$a_{avg} = \frac{-3 - 5}{4} = -2 m/s$^2$$

Question 12

Which of the following best describes the difference between average velocity and instantaneous velocity?

Accepted Answer

Average velocity is calculated over a finite time interval, while instantaneous velocity is the velocity at a specific instant.

Question 13

A car moves along a straight road. Its position as a function of time is shown in a position-time graph. At which point is the car's instantaneous velocity zero?

Accepted Answer

At the peak (maximum) of the position-time graph.

Question 14

If a particle's velocity-time graph is a straight line with a positive slope, what can you say about the particle's acceleration?

Accepted Answer

The particle has a constant positive acceleration.

Question 15

A cyclist travels 3 km east, then 4 km west, and finally 2 km east. What is the total distance traveled and the displacement?

Accepted Answer

Distance = 9 km, Displacement = 1 km east

Question 16

Which of the following is the correct SI unit for acceleration?

Accepted Answer

$$	ext{m/s}^2$$

One-Dimensional Kinematics: Position, Displacement, Velocity, and Acceleration

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