Q: A car travels 120 km in 2 hours. What is its average speed, and how does this differ from its average velocity if it 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 vector $$ extbf{A}$$ has a magnitude of $$5$$ units and points $$53^ ext{o}$$ above the positive x-axis. What are its components in unit vector form?

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

Q: A projectile is launched at an angle of $$30^ ext{o}$$ with an initial speed of $$20\ \text{m/s}. $$What is the horizontal component of its velocity?

$$20 \cos 30^ ext{o} = 17.3\ \text{m/s}$$

Q: A cyclist moves in a circle of radius $$10\ \text{m} at a $$constant speed of $$5\ \text{m/s}. $$What is the period $$T of $$the motion?

$$T = \frac{2\pi r}{v} = \frac{2\pi \times 10}{5} = 4\pi\ \text{s}$$

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

Accepted Answer

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

Question 4

Which of the following statements about significant figures is correct?

Accepted Answer

The number of significant figures in a calculated result should reflect the precision of the least precise measurement used.

Question 5

A ball is thrown vertically upward with an initial velocity of $$10\ 	ext{m/s}. $$Using the kinematic equations, what is the maximum height reached? (Assume $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$5.1\ 	ext{m}$$

Question 6

Which equation correctly expresses the relationship between displacement ($$\Delta x$$), initial velocity ($$v_0$$), acceleration ($$a$$), and time ($$t) $$for constant acceleration?

Accepted Answer

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

Question 7

A projectile is launched at an angle of $$30^	ext{o}$$ with an initial speed of $$20\ 	ext{m/s}. $$What is the horizontal component of its velocity?

Accepted Answer

$$20 \cos 30^	ext{o} = 17.3\ 	ext{m/s}$$

Question 8

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

Accepted Answer

The vertical acceleration is constant and equal to $$-g.$$

Question 9

A runner accelerates from rest at $$2\ 	ext{m/s}^2$$ for $$4$$ seconds. What is her final velocity?

Accepted Answer

$$8\ 	ext{m/s}$$

Question 10

Which of the following best defines 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 cyclist moves in a circle of radius $$10\ 	ext{m} at a $$constant speed of $$5\ 	ext{m/s}. $$What is the period $$T of $$the motion?

Accepted Answer

$$T = \frac{2\pi r}{v} = \frac{2\pi 	imes 10}{5} = 4\pi\ 	ext{s}$$

Question 12

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 13

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: $$10$$; Direction: $$-53^	ext{o} ($$below x-axis)

Question 14

A stone is dropped from a bridge and hits the water after $$2$$ seconds. What is its velocity just before impact? (Assume $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$19.6\ 	ext{m/s}$$ downward

Question 15

Which of the following best describes 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.

Question 16

A projectile is launched horizontally from a $$45\ 	ext{m}$$ high cliff. How long does it take to hit the ground? (Assume $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 	imes 45}{9.8}} \approx 3.03\ 	ext{s}$$

Question 17

Which of the following is the correct expression for angular speed $$\omega in $$terms of period $$T$$?

Accepted Answer

$$\omega = \frac{2\pi}{T}$$

Question 18

A car moves east at $$20\ 	ext{m/s}$$ for $$10$$ seconds, then north at $$20\ 	ext{m/s}$$ for $$10$$ seconds. What is the magnitude of its displacement from the starting point?

Accepted Answer

$$\sqrt{(200)^2$ + (200)^2$} = 283\ 	ext{m}$$

Question 19

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

Accepted Answer

Objects in free fall experience a constant acceleration of $$-9.8\ 	ext{m/s}^2$$ downward.

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

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