Q: A car travels 120 km in 2 hours. What is its average speed, and how does this differ from its average velocity if the car returns to its starting point?

Average speed is $$60\ \text{km/h}$$; average velocity is $$0\ \text{km/h}$$ because displacement is zero.

Q: A projectile is launched from ground level with an initial velocity of $$v_0 = 20$$\ \text{m/s}$$ at an angle of 30$$^\circ$$ above the horizontal. What is the horizontal component of its initial velocity?

$$v_{0x} = v_0$ \cos\theta = 20 \cos 30^\circ = 17.32\ \text{m/s}$$

Q: A vector $$ extbf{A}$$ has a magnitude of $$5$$ units and points $$53^\circ$$ above the x-axis. What are its components in unit vector form?

$$\textbf{A} = 3\hat{i} + 4\hat{j}$$

Q: A ball is thrown vertically upward with an initial velocity of $$15\ \text{m/s}. $$Using the kinematic equation $$v = v_0$ + at$$, how long does it take for the ball to reach its maximum height?

$$t = \frac{-v_0$}{a} = \frac{-15}{-9.8} = 1.53\ \text{s}$$

Q: A cyclist accelerates from rest at $$2\ \text{m/s}^2$$ for $$5\ \text{s}. $$What is the cyclist's displacement during this time?

$$x = v_0$ t + \frac{1}{2} a t^2$ = 0 + \frac{1}{2} \times 2 \times 25 = 25\ \text{m}$$

Q: A vector $$ extbf{B} is $$given by $$\textbf{B} = 6\hat{i} - 8\hat{j}. $$What is its magnitude and direction relative to the positive x-axis?

Magnitude: $$10$$ units; Direction: $$\theta = \arctan\left(\frac{-8}{6}\right) = -53^\circ$$ below the x-axis.

Question 1

A car travels 120 km in 2 hours. What is its average speed, and how does this differ from its average velocity if the car returns to its starting point?

Accepted Answer

Average speed is $$60\ 	ext{km/h}$$; average velocity is $$0\ 	ext{km/h}$$ because displacement is zero.

Question 2

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

Accepted Answer

Displacement is the straight-line change in position, while distance is the total length of the path traveled.

Question 3

A projectile is launched from ground level with an initial velocity of $$v_0 = 20$$\ 	ext{m/s}$$ at an angle of 30$$^\circ$$ above the horizontal. What is the horizontal component of its initial velocity?

Accepted Answer

$$v_{0x} = v_0$ \cos	heta = 20 \cos 30^\circ = 17.32\ 	ext{m/s}$$

Question 4

Which of the following statements about free fall on planet Earth is correct?

Accepted Answer

The acceleration due to gravity is constant and directed downward, $$a = -9.8\ 	ext{m/s}^2.$$

Question 5

A vector $$	extbf{A}$$ has a magnitude of $$5$$ units and points $$53^\circ$$ above the x-axis. What are its components in unit vector form?

Accepted Answer

$$	extbf{A} = 3\hat{i} + 4\hat{j}$$

Question 6

A student measures the length of a rod as $$12.30\ 	ext{cm}$$, $$12.3\ 	ext{cm}$$, and $$12.300\ 	ext{cm}. $$Which measurement has the greatest number of significant figures?

Accepted Answer

$$12.300\ 	ext{cm}$$

Question 7

A ball is thrown vertically upward with an initial velocity of $$15\ 	ext{m/s}. $$Using the kinematic equation $$v = v_0$ + at$$, how long does it take for the ball to reach its maximum height?

Accepted Answer

$$t = \frac{-v_0$}{a} = \frac{-15}{-9.8} = 1.53\ 	ext{s}$$

Question 8

Which of the following is always true for projectile motion on planet Earth (neglecting air resistance)?

Accepted Answer

The horizontal acceleration is zero, and the vertical acceleration is $$-9.8\ 	ext{m/s}^2.$$

Question 9

A cyclist accelerates from rest at $$2\ 	ext{m/s}^2$$ for $$5\ 	ext{s}. $$What is the cyclist's displacement during this time?

Accepted Answer

$$x = v_0$ t + \frac{1}{2} a t^2$ = 0 + \frac{1}{2} 	imes 2 	imes 25 = 25\ 	ext{m}$$

Question 10

Which of the following best describes centripetal acceleration in uniform circular motion?

Accepted Answer

It is directed toward the center of the circle and has magnitude $$a_c = \frac{v^2$}{r}.$$

Question 11

A vector $$	extbf{B} is $$given by $$	extbf{B} = 6\hat{i} - 8\hat{j}. $$What is its magnitude and direction relative to the positive x-axis?

Accepted Answer

Magnitude: $$10$$ units; Direction: $$	heta = \arctan\left(\frac{-8}{6}ight) = -53^\circ$$ below the x-axis.

Question 12

A runner moves along a straight path. At $$t = 0$$, she is at $$x = 0. At$$ $$t = 5\ 	ext{s}$$, she is at $$x = 20\ 	ext{m}. $$What is her average velocity?

Accepted Answer

$$v_{avg} = \frac{\Delta x}{\Delta t} = \frac{20}{5} = 4\ 	ext{m/s}$$

Question 13

A stone is dropped from a height of $$45\ 	ext{m}. $$How long does it take to reach the ground? (Use $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{90}{9.8}} = 3.03\ 	ext{s}$$

Question 14

Which of the following is NOT a correct application of dimensional analysis?

Accepted Answer

Adding quantities with different units, such as meters and seconds.

Question 15

A car moves in a circle of radius $$10\ 	ext{m} at a $$constant speed of $$5\ 	ext{m/s}. $$What is its centripetal acceleration?

Accepted Answer

$$a_c = \frac{v^2$}{r} = \frac{25}{10} = 2.5\ 	ext{m/s}^2$$

Question 16

A wheel completes one revolution every $$2\ 	ext{s}. $$What is its angular speed $$\omega$$?

Accepted Answer

$$\omega = \frac{2\pi}{T} = \frac{2\pi}{2} = \pi\ 	ext{rad/s}$$

Question 17

A car accelerates from $$10\ 	ext{m/s} to$$ $$30\ 	ext{m/s} in$$ $$4\ 	ext{s}. $$What is its average acceleration?

Accepted Answer

$$a_{avg} = \frac{\Delta v}{\Delta t} = \frac{30 - 10}{4} = 5\ 	ext{m/s}^2$$

Question 18

A projectile is launched horizontally from a $$20\ 	ext{m}$$ high cliff with a speed of $$5\ 	ext{m/s}. $$How far from the base of the cliff does it land? (Use $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

Time to fall: $$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{40}{9.8}} = 2.02\ 	ext{s}$$; Range: $$x = v t = 5 	imes 2.02 = 10.1\ 	ext{m}$$

Question 19

Which of the following is a correct statement about radial and tangential acceleration in circular motion?

Accepted Answer

Radial acceleration points toward the center; tangential acceleration is perpendicular to radial and changes the speed.

PHYS 180 Study Guide: Chapters 1–4 (Units, Kinematics, Vectors, and Circular Motion)

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