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?

$$v_{0x} = v_0$ \cos 30^\circ = 20 \times 0.866 = 17.32\ \text{m/s}$$

Q: A student measures the length of a rod as $$12.34\ \text{cm}$$, $$12.3\ \text{cm}$$, and $$12.345\ \text{cm}. $$Which measurement has the greatest number of significant figures?

$$12.345\ \text{cm}$$ has 5 significant figures.

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 final velocity using the kinematic equation $$v = v_0$ + at$$?

$$v = 0 + 2 \times 5 = 10\ \text{m/s}$$

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 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 a vector quantity representing the change in position, while distance is a scalar quantity representing the total path length.

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

$$v_{0x} = v_0$ \cos 30^\circ = 20 	imes 0.866 = 17.32\ 	ext{m/s}$$

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, with $$a = -9.8\ 	ext{m/s}^2.$$

Question 5

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

Accepted Answer

$$A_x = 5 \cos 53^\circ = 3.0$$, $$A_y = 5 \sin 53^\circ = 4.0$$

Question 6

A student measures the length of a rod as $$12.34\ 	ext{cm}$$, $$12.3\ 	ext{cm}$$, and $$12.345\ 	ext{cm}. $$Which measurement has the greatest number of significant figures?

Accepted Answer

$$12.345\ 	ext{cm}$$ has 5 significant figures.

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 vector $$	extbf{B} is $$given in unit vector form as $$	extbf{B} = 2\hat{i} + 3\hat{j}. $$What is its magnitude and direction relative to the x-axis?

Accepted Answer

Magnitude: $$\sqrt{2^2$ + 3^2$} = \sqrt{13} = 3.61$$; Direction: $$	heta = 	an$$^{-1}$$(\frac{3}{2}) = 56.3^\circ$$

Question 10

A cyclist accelerates from rest at $$2\ 	ext{m/s}^2$$ for $$5\ 	ext{s}. $$What is the final velocity using the kinematic equation $$v = v_0$ + at$$?

Accepted Answer

$$v = 0 + 2 	imes 5 = 10\ 	ext{m/s}$$

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

It always points toward the center of the circle.

Question 13

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 14

A stone is dropped from a height of $$45\ 	ext{m}. $$How long does it take to reach the ground? (Use $$y = y_0$ + v_0$ t + \frac{1}{2} a t^2$ with v_0$ = 0$$, $$a = -9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$t = \sqrt{\frac{2 	imes 45}{9.8}} = \sqrt{9.18} = 3.03\ 	ext{s}$$

Question 15

A particle moves in a circle of radius $$r$$ with angular speed $$\omega. $$What is the period $$T of $$its motion?

Accepted Answer

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

Question 16

A car travels $$100\ 	ext{km} at$$ $$50\ 	ext{km/h}$$, then $$50\ 	ext{km} at$$ $$100\ 	ext{km/h}. $$What is the average speed for the entire trip?

Accepted Answer

Total time: $$\frac{100}{50} + \frac{50}{100} = 2 + 0.5 = 2.5\ 	ext{h}$$; Average speed: $$\frac{150}{2.5} = 60\ 	ext{km/h}$$

Question 17

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 18

A vector $$	extbf{C} is $$given as $$	extbf{C} = 4\hat{i} - 3\hat{j}. $$What is its magnitude and direction relative to the x-axis?

Accepted Answer

Magnitude: $$\sqrt{4^2$ + (-3)^2$} = 5$$; Direction: $$	heta = 	an$$^{-1}$$(\frac{-3}{4}) = -36.9^\circ$$

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

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