Q: A ball is thrown straight up with an initial velocity of $$v_0 = 12$$\ \mathrm{m/s}$$. Neglecting air resistance, what is the maximum height reached by the ball? (Use g = 9.8$$\ \mathrm{$$m/s^2$$}$$)

$$h = \frac{v_0$^2}{2g} = \frac{(12)^2$}{2 \times 9.8} = 7.35\ \mathrm{m}$$

Q: A car starts from rest and accelerates uniformly at $$a = 3\ \mathrm{m/s^2$}$$ for $$4\ \mathrm{s}. $$What is its final velocity?

$$v = v_0$ + at = 0 + 3 \times 4 = 12\ \mathrm{m/s}$$

Question 1

A car moves along a straight road such that its position-versus-time graph is a straight line with a positive slope. Which of the following statements is true about the car's motion?

Accepted Answer

The car is moving at a constant velocity in the positive direction.

Question 2

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

Accepted Answer

Distance is a scalar and measures the total path length; displacement is a vector and measures the straight-line change from initial to final position.

Question 3

A runner jogs 100 m east, then 60 m west. What is the runner's displacement?

Accepted Answer

$$40\ \mathrm{m}$$ east

Question 4

The position of a particle is given by $$x(t) = 4t^2$ - 2t + 1 (in $$meters, with $$t in $$seconds). What is the instantaneous velocity at $$t = 3\ \mathrm{s}$$?

Accepted Answer

$$v = 22\ \mathrm{m/s}$$

Question 5

A car moves with a constant velocity of $$-5\ \mathrm{m/s}$$ for $$8\ \mathrm{s}. If it $$starts at $$x_0 = 20$$\ \mathrm{m}$$, what is its position after 8$$\ \mathrm{s}$$?

Accepted Answer

$$x = -20\ \mathrm{m}$$

Question 6

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

Accepted Answer

Velocity is a vector and can be negative; speed is a scalar and always positive.

Question 7

A ball is thrown straight up with an initial velocity of $$v_0 = 12$$\ \mathrm{m/s}$$. Neglecting air resistance, what is the maximum height reached by the ball? (Use g = 9.8$$\ \mathrm{$$m/s^2$$}$$)

Accepted Answer

$$h = \frac{v_0$^2}{2g} = \frac{(12)^2$}{2 	imes 9.8} = 7.35\ \mathrm{m}$$

Question 8

The area under a velocity-versus-time graph between $$t_1$$ and $$t_2$$ represents:

Accepted Answer

The displacement of the object between $$t_1$$ and $$t_2$$

Question 9

A car starts from rest and accelerates uniformly at $$a = 3\ \mathrm{m/s^2$}$$ for $$4\ \mathrm{s}. $$What is its final velocity?

Accepted Answer

$$v = v_0$ + at = 0 + 3 	imes 4 = 12\ \mathrm{m/s}$$

Question 10

A cyclist travels at $$5\ \mathrm{m/s}$$ for $$10\ \mathrm{s}$$, then at $$-3\ \mathrm{m/s}$$ for $$4\ \mathrm{s}. $$What is the total displacement?

Accepted Answer

$$38\ \mathrm{m}$$

Question 11

A position-versus-time graph for an object is a horizontal line. What does this indicate about the object's motion?

Accepted Answer

The object is at rest.

Question 12

A drag racer starts from rest and accelerates uniformly, reaching a velocity of $$30\ \mathrm{m/s} in$$ $$4\ \mathrm{s}. $$What is the acceleration?

Accepted Answer

$$a = \frac{\Delta v}{\Delta t} = \frac{30}{4} = 7.5\ \mathrm{m/s^2$}$$

Question 13

A ball is dropped from a height of $$20\ \mathrm{m}. $$Neglecting air resistance, how long does it take to reach the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{40}{9.8}} \approx 2.02\ \mathrm{s}$$

Question 14

Which of the following is the correct kinematic equation for position under constant acceleration?

Accepted Answer

$$x = x_0$ + v_0$ t + \frac{1}{2} a t^2$

Question 15

A car moves with a velocity given by $$v(t) = 6 - 2t (in m/s). $$What is the car's acceleration?

Accepted Answer

$$a = -2\ \mathrm{m/s^2$}$$

Question 16

A particle moves such that its velocity-versus-time graph is a straight line with a negative slope. What does this indicate about the particle's acceleration?

Accepted Answer

The particle has a constant negative acceleration.

Question 17

A springbok leaps vertically upward with an initial velocity of $$7.0\ \mathrm{m/s}. $$What is the maximum height it reaches? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$h = \frac{v_0$^2}{2g} = \frac{(7.0)^2$}{2 	imes 9.8} = 2.5\ \mathrm{m}$$

Question 18

A car's velocity changes from $$10\ \mathrm{m/s} to$$ $$-2\ \mathrm{m/s} in$$ $$4\ \mathrm{s}. $$What is its average acceleration?

Accepted Answer

$$a = \frac{-2 - 10}{4} = -3\ \mathrm{m/s^2$}$$

Question 19

A ball rolls up a ramp and then back down. Which of the following statements is true about its acceleration while on the ramp (neglecting friction)?

Accepted Answer

The acceleration is constant and directed down the ramp.

Kinematics in One Dimension: Study Notes

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드