Q: A car starts from rest and accelerates at $$2\ \mathrm{m/s^2$}$$ for $$10\ \mathrm{s}. $$What is its displacement during this time?

$$x = v_i t + \frac{1}{2} a t^2$ = 0 + \frac{1}{2} \times 2 \times 10^2$ = 100\ \mathrm{m}$$

Q: A rock is dropped from a height of $$20\ \mathrm{m} ($$see Figure 2.26). What is its velocity just before it hits the ground? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{2 g h} = \sqrt{2 \times 9.8 \times 20} = 19.8\ \mathrm{m/s}$$

Q: If $$v_x = -6\ \mathrm{m/s}$$ and $$a_x = +2\ \mathrm{m/s^2$}$$, what is the velocity after $$2\ \mathrm{s}$$?

$$v = -6 + 2 \times 2 = -2\ \mathrm{m/s}$$

Question 1

A Japanese 'bullet train' accelerates from rest to 300 km/h in 5 minutes. Assuming constant acceleration, what is the magnitude of its acceleration in $$\mathrm{m/s^2$}$$?

Accepted Answer

$$a = \dfrac{83.33\ \mathrm{m/s}}{300\ \mathrm{s}} = 0.278\ \mathrm{m/s^2$}$$

Question 2

Refer to the velocity-time graph for the basketball player (Figure 2.20). What is the acceleration between $$t = 0$$ and $$t = 6\ \mathrm{s}$$?

Accepted Answer

$$a = \dfrac{6\ \mathrm{m/s} - 0\ \mathrm{m/s}}{6\ \mathrm{s} - 0\ \mathrm{s}} = 1\ \mathrm{m/s^2$}$$

Question 3

A car starts from rest and accelerates at $$2\ \mathrm{m/s^2$}$$ for $$10\ \mathrm{s}. $$What is its displacement during this time?

Accepted Answer

$$x = v_i t + \frac{1}{2} a t^2$ = 0 + \frac{1}{2} 	imes 2 	imes 10^2$ = 100\ \mathrm{m}$$

Question 4

A rock is dropped from a height of $$20\ \mathrm{m} ($$see Figure 2.26). What is its velocity just before it hits the ground? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2 g h} = \sqrt{2 	imes 9.8 	imes 20} = 19.8\ \mathrm{m/s}$$

Question 5

A shuttle deploys a parachute after landing and slows down while moving forward. What is the direction of its velocity and acceleration?

Accepted Answer

Velocity and acceleration point in opposite directions.

Question 6

A ball is thrown straight upward. At its highest point, what are its velocity and acceleration? (Ignore air resistance.)

Accepted Answer

$$v_y = 0,\ a_y = -g$$

Question 7

A car travels at a constant velocity of $$20\ \mathrm{m/s}$$ past a stationary car. The stationary car immediately accelerates at $$5.0\ \mathrm{m/s^2$}. $$How far does the accelerating car travel before overtaking the first car?

Accepted Answer

Question 8

Which of the following is true about the acceleration of an object in free fall near Earth's surface (neglecting air resistance)?

Accepted Answer

The acceleration is always $$-9.8\ \mathrm{m/s^2$}.$$

Question 9

Given the acceleration graph in Figure 2.37, how do you find the change in velocity between $$t = 0$$ and $$t = 10\ \mathrm{s}$$?

Accepted Answer

By calculating the area under the acceleration-time curve.

Question 10

A velocity-time graph is a straight line with a negative slope. What does this indicate about the object's motion?

Accepted Answer

The object is decelerating (negative acceleration).

Question 11

A car leaves a stop sign and its velocity increases non-linearly, as shown in Figure 2.36. What does the shape of the acceleration graph indicate?

Accepted Answer

Acceleration is decreasing.

Question 12

If $$v_x = -6\ \mathrm{m/s}$$ and $$a_x = +2\ \mathrm{m/s^2$}$$, what is the velocity after $$2\ \mathrm{s}$$?

Accepted Answer

$$v = -6 + 2 	imes 2 = -2\ \mathrm{m/s}$$

Question 13

Which kinematic equation would you use to find the final velocity of an object given its initial velocity, acceleration, and displacement, but not time?

Accepted Answer

$$v_f^2$ = v_i^2$ + 2 a \Delta x$$

Question 14

A rock is thrown straight downward from a bridge. What is the magnitude of its acceleration just after release and just before impact (neglect air resistance)?

Accepted Answer

Equal to $$g at $$both times.

Question 15

The area under a velocity-time graph represents:

Accepted Answer

Displacement

Question 16

If the velocity and acceleration of an object have opposite signs, what happens to the object's speed?

Accepted Answer

It decreases.

Question 17

A car accelerates from $$0 to$$ $$30\ \mathrm{m/s} in$$ $$10\ \mathrm{s}. $$What is its average acceleration?

Accepted Answer

$$a = \dfrac{30}{10} = 3\ \mathrm{m/s^2$}$$

Kinematics in One Dimension: Acceleration, Motion, and Applications

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