Q: A truck accelerates forward from $$3.0\ \mathrm{m/s} at a $$uniform $$0.4\ \mathrm{m/s^2$}. It $$travels a distance of $$2\ \mathrm{km}$$ while accelerating. How fast is the truck moving just as it has traveled the $$2\ \mathrm{km}$$?

$$v_f = \sqrt{v_i^2$ + 2a(x_f - x_i)} = \sqrt{(3.0)^2$ + 2 \times 0.4 \times 2000} = 56.6\ \mathrm{m/s}$$

Q: A bullet is fired straight up with a speed of $$25\ \mathrm{m/s}. $$Assuming negligible air resistance, how long does it take to return to its starting point?

$$t = \frac{2v_0}{g} = \frac{2 \times 25}{9.8} = 5.1\ \mathrm{s}$$

Q: A ball is thrown downward from the top of a building with an initial speed of $$20\ \mathrm{m/s}. It $$strikes the ground after $$2.0\ \mathrm{s}. $$What is the height of the building?

$$y = v_i t + \frac{1}{2} a t^2$ = 20 \times 2.0 + 0.5 \times 9.8 \times (2.0)^2$ = 40 + 19.6 = 59.6\ \mathrm{m}$$

Q: A free-fall ride at an amusement park starts at rest and is in free fall. What is the velocity of the ride after $$2.3\ \mathrm{s}$$?

$$v = v_0$ + a t = 0 + 9.8 \times 2.3 = 22.5\ \mathrm{m/s}$$ downward

Question 1

A car travels 5 m east, stops, turns around, and travels 5 m west. What is the car's displacement?

Accepted Answer

0 m

Question 2

Which of the following quantities is a vector?

Accepted Answer

velocity

Question 3

A ball is thrown straight up, reaches a maximum height, then falls to its initial height. Which statement is correct about the direction of velocity and acceleration as it is going up?

Accepted Answer

Its velocity points upward and its acceleration points downward.

Question 4

A truck accelerates forward from $$3.0\ \mathrm{m/s} at a $$uniform $$0.4\ \mathrm{m/s^2$}. It $$travels a distance of $$2\ \mathrm{km}$$ while accelerating. How fast is the truck moving just as it has traveled the $$2\ \mathrm{km}$$?

Accepted Answer

$$v_f = \sqrt{v_i^2$ + 2a(x_f - x_i)} = \sqrt{(3.0)^2$ + 2 	imes 0.4 	imes 2000} = 56.6\ \mathrm{m/s}$$

Question 5

An athlete circles 10 times around a circular 2.0-km track in 110 min. What is the athlete's average velocity for the ten laps?

Accepted Answer

$$v_{avg} = 0\ \mathrm{km/min}$$

Question 6

A bullet is fired straight up with a speed of $$25\ \mathrm{m/s}. $$Assuming negligible air resistance, how long does it take to return to its starting point?

Accepted Answer

$$t = \frac{2v_0}{g} = \frac{2 	imes 25}{9.8} = 5.1\ \mathrm{s}$$

Question 7

A ball is thrown downward from the top of a building with an initial speed of $$20\ \mathrm{m/s}. It $$strikes the ground after $$2.0\ \mathrm{s}. $$What is the height of the building?

Accepted Answer

$$y = v_i t + \frac{1}{2} a t^2$ = 20 	imes 2.0 + 0.5 	imes 9.8 	imes (2.0)^2$ = 40 + 19.6 = 59.6\ \mathrm{m}$$

Question 8

A velocity-time table represents the motion of a rightward-moving motorcycle. At $$t = 0.0\ \mathrm{s}$$, $$v = 26.0\ \mathrm{m/s}$$; at $$t = 8.0\ \mathrm{s}$$, $$v = 2.4\ \mathrm{m/s}. $$What is the magnitude and direction of the average acceleration?

Accepted Answer

$$a_{avg} = \frac{v_f - v_i}{t_f - t_i} = \frac{2.4 - 26.0}{8.0 - 0.0} = -2.95\ \mathrm{m/s^2$}$$, leftward

Question 9

A motorist travels $$160\ \mathrm{km} at$$ $$80.0\ \mathrm{km/h}$$, stops for $$30.0\ \mathrm{min}$$, then travels another $$120\ \mathrm{km} at$$ $$100\ \mathrm{km/h}. $$What is the average speed of the motorist for this trip?

Accepted Answer

$$v_{avg} = \frac{160 + 120}{\frac{160}{80} + 0.5 + \frac{120}{100}} = \frac{280}{2 + 0.5 + 1.2} = \frac{280}{3.7} = 75.7\ \mathrm{km/h}$$

Question 10

A coin is flipped straight up. What is the velocity and acceleration of the coin at the top of its trajectory?

Accepted Answer

Velocity is zero, acceleration is $$-9.8\ \mathrm{m/s^2$}$$ downward.

Question 11

A free-fall ride at an amusement park starts at rest and is in free fall. What is the velocity of the ride after $$2.3\ \mathrm{s}$$?

Accepted Answer

$$v = v_0$ + a t = 0 + 9.8 	imes 2.3 = 22.5\ \mathrm{m/s}$$ downward

Question 12

A bullet moving horizontally with a speed of $$200\ \mathrm{m/s}$$ strikes a wall and penetrates a distance of $$3.0\ \mathrm{cm}. $$What is the magnitude of the average acceleration of the bullet in the wall?

Accepted Answer

$$a = \frac{v_f^2$ - v_i^2$}{2d} = \frac{0^2$ - (200)^2$}{2 	imes 0.03} = -666,667\ \mathrm{m/s^2$}$$

Question 13

A ball is thrown straight up with an initial velocity of $$15\ \mathrm{m/s}. $$What is the maximum height it reaches?

Accepted Answer

$$h = \frac{v_0$^2}{2g} = \frac{(15)^2$}{2 	imes 9.8} = 11.5\ \mathrm{m}$$

Question 14

A car travels $$100\ \mathrm{km}$$ east, $$50\ \mathrm{km}$$ west, and $$30\ \mathrm{km}$$ north. What is the magnitude of its displacement?

Accepted Answer

$$d = \sqrt{(100 - 50)^2$ + 30^2$} = \sqrt{50^2$ + 30^2$} = \sqrt{2500 + 900} = \sqrt{3400} = 58.3\ \mathrm{km}$$

Question 15

A position-time graph shows a straight line with a positive slope. What does this indicate about the object's motion?

Accepted Answer

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

Question 16

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

Accepted Answer

The object is moving in the positive direction and slowing down, eventually stopping and reversing direction.

Question 17

A car accelerates from rest at $$2.0\ \mathrm{m/s^2$}$$ for $$5.0\ \mathrm{s}. $$What is its final velocity?

Accepted Answer

$$v = v_0$ + a t = 0 + 2.0 	imes 5.0 = 10.0\ \mathrm{m/s}$$

Question 18

A student drops a ball from a height of $$20\ \mathrm{m}. $$How long does it take to reach the ground? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$y = \frac{1}{2} g t^2$ \Rightarrow t = \sqrt{\frac{2y}{g}} = \sqrt{\frac{40}{9.8}} = 2.02\ \mathrm{s}$$

Kinematics and Measurement: Study Guide for Introductory Physics (Chapters 1-3)

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