Q: A car travels from $$x_1 = 10$$\ \text{m}$$ to x_2$ = 40\ \text{m} in$$ $$t_1 = 2$$\ \text{s}$$ to t_2$ = 5\ \text{s}. $$What is the car's average velocity?

$$v_{\text{av}} = \frac{40 - 10}{5 - 2} = \frac{30}{3} = 10\ \text{m/s}$$

Q: A runner moves from $$x_1 = 0$$\ \text{m}$$ to x_2$ = 100\ \text{m}$$ and then back to $$x_1 = 0$$\ \text{m}$$. What is the displacement and the total distance traveled?

Displacement: $$0\ \text{m}$$, Distance: $$200\ \text{m}$$

Q: A particle's position is given by $$x(t) = 3t^2$ + 2t. $$What is its instantaneous velocity at $$t = 2\ \text{s}$$?

$$v = \frac{dx}{dt} = 6t + 2 \Rightarrow v(2) = 6 \times 2 + 2 = 14\ \text{m/s}$$

Q: If a particle moves from $$x_1 = 5$$\ \text{m}$$ to x_2$ = 15\ \text{m} in$$ $$t_1 = 0$$\ \text{s}$$ to t_2$ = 2\ \text{s}$$, what is its average speed?

$$\text{Average speed} = \frac{\text{Distance}}{\text{Time}} = \frac{10\ \text{m}}{2\ \text{s}} = 5\ \text{m/s}$$

Q: A car's velocity changes from $$v_1 = 20$$\ \text{m/s}$$ to v_2$ = 60\ \text{m/s} in$$ $$t_1 = 0$$\ \text{s}$$ to t_2$ = 4\ \text{s}. $$What is its average acceleration?

$$a_{\text{av}} = \frac{60 - 20}{4 - 0} = \frac{40}{4} = 10\ \text{m/s}^2$$

Q: A cyclist moves along a straight path. At $$t = 0\ \text{s}$$, her velocity is $$v_1 = 5$$\ \text{m/s}$$, and at t = 10$$\ \text{s}$$, her velocity is v_2$ = -5\ \text{m/s}. $$What is her average acceleration?

$$a_{\text{av}} = \frac{-5 - 5}{10 - 0} = \frac{-10}{10} = -1\ \text{m/s}^2$$

Question 1

A car travels from $$x_1 = 10$$\ 	ext{m}$$ to x_2$ = 40\ 	ext{m} in$$ $$t_1 = 2$$\ 	ext{s}$$ to t_2$ = 5\ 	ext{s}. $$What is the car's average velocity?

Accepted Answer

$$v_{	ext{av}} = \frac{40 - 10}{5 - 2} = \frac{30}{3} = 10\ 	ext{m/s}$$

Question 2

A runner moves from $$x_1 = 0$$\ 	ext{m}$$ to x_2$ = 100\ 	ext{m}$$ and then back to $$x_1 = 0$$\ 	ext{m}$$. What is the displacement and the total distance traveled?

Accepted Answer

Displacement: $$0\ 	ext{m}$$, Distance: $$200\ 	ext{m}$$

Question 3

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

Accepted Answer

Average speed is the total distance traveled divided by time, while average velocity is the displacement divided by time.

Question 4

A particle's position is given by $$x(t) = 3t^2$ + 2t. $$What is its instantaneous velocity at $$t = 2\ 	ext{s}$$?

Accepted Answer

$$v = \frac{dx}{dt} = 6t + 2 \Rightarrow v(2) = 6 	imes 2 + 2 = 14\ 	ext{m/s}$$

Question 5

If a particle moves from $$x_1 = 5$$\ 	ext{m}$$ to x_2$ = 15\ 	ext{m} in$$ $$t_1 = 0$$\ 	ext{s}$$ to t_2$ = 2\ 	ext{s}$$, what is its average speed?

Accepted Answer

$$	ext{Average speed} = \frac{	ext{Distance}}{	ext{Time}} = \frac{10\ 	ext{m}}{2\ 	ext{s}} = 5\ 	ext{m/s}$$

Question 6

On a position-time graph, what does the slope of the tangent at a point represent?

Accepted Answer

The instantaneous velocity at that point.

Question 7

A car's velocity changes from $$v_1 = 20$$\ 	ext{m/s}$$ to v_2$ = 60\ 	ext{m/s} in$$ $$t_1 = 0$$\ 	ext{s}$$ to t_2$ = 4\ 	ext{s}. $$What is its average acceleration?

Accepted Answer

$$a_{	ext{av}} = \frac{60 - 20}{4 - 0} = \frac{40}{4} = 10\ 	ext{m/s}^2$$

Question 8

If the velocity of a particle is given by $$v(t) = 4t - 3$$, what is its instantaneous acceleration?

Accepted Answer

$$a = \frac{dv}{dt} = 4$$

Question 9

A cyclist moves along a straight path. At $$t = 0\ 	ext{s}$$, her velocity is $$v_1 = 5$$\ 	ext{m/s}$$, and at t = 10$$\ 	ext{s}$$, her velocity is v_2$ = -5\ 	ext{m/s}. $$What is her average acceleration?

Accepted Answer

$$a_{	ext{av}} = \frac{-5 - 5}{10 - 0} = \frac{-10}{10} = -1\ 	ext{m/s}^2$$

Question 10

Which scenario best illustrates the concept of instantaneous velocity?

Accepted Answer

Reading the speedometer of a car at a specific instant.

Question 11

A particle moves along the x-axis. If its velocity is positive and increasing, what can be said about its acceleration?

Accepted Answer

Acceleration is positive; the particle is speeding up in the $$+x$$ direction.

Question 12

If a position-time graph has a negative slope, what does this indicate about the particle's motion?

Accepted Answer

The particle is moving in the $$-x$$ direction.

Question 13

A car travels 100 m east, then 100 m west, all in 20 seconds. What is its average velocity?

Accepted Answer

$$v_{	ext{av}} = \frac{0}{20} = 0\ 	ext{m/s}$$

Question 14

A position-time graph shows a curve with a tangent slope of zero at point C. What is the velocity at point C?

Accepted Answer

$$v_x = 0$$

Question 15

A velocity-time graph shows a tangent slope of zero at point C. What is the acceleration at point C?

Accepted Answer

$$a_x = 0$$

Question 16

A particle's velocity is given by $$v_x(t) = 2t^2$. What is its instantaneous acceleration at t = 3$$\ 	ext{s}$$?

Accepted Answer

$$a_x = \frac{dv_x}{dt} = 4t \Rightarrow a_x(3) = 4 	imes 3 = 12\ 	ext{m/s}^2$$

Question 17

A car's odometer reads 14,372 miles. If the car travels 100 miles forward and then 100 miles back, what will the odometer read?

Accepted Answer

14,572 miles

Question 18

Which of the following statements about speed and velocity is correct?

Accepted Answer

Speed is a scalar and does not have direction, while velocity is a vector and has direction.

Kinematics in One Dimension: Position, Velocity, and Acceleration

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