Q: A car travels 120 km in 2 hours. What is its average speed, and which units should be used to express the answer according to proper dimensional analysis?

$$60\ \text{km/h}$$; units of speed are always length/time$

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

$$h = \frac{v_0$^2}{2g} = \frac{(10)^2$}{2 \times 9.8} = 5.1\ \text{m}$$

Q: A vector $$\vec{B} is $$given as $$\vec{B} = 3\hat{i} + 4\hat{j}. $$What is the magnitude and direction (angle with respect to the x-axis) of $$\vec{B}$$?

Magnitude: $$5$$; Direction: $$\theta = \arctan\left(\frac{4}{3}\right) \approx 53^\circ$$

Q: A train accelerates from rest at $$2\ \text{m/s}^2$$ for $$5$$ seconds. What is its final velocity?

$$v = v_0$ + at = 0 + 2 \times 5 = 10\ \text{m/s}$$

Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$What is the time of flight before it lands back at the same height? (Neglect air resistance)

$$T = \frac{2v_0\sin\theta}{g}$$

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

$$T = \frac{2\pi r}{v} = \frac{2\pi \times 10}{5} = 4\pi \approx 12.6\ \text{s}$$

Question 1

A car travels 120 km in 2 hours. What is its average speed, and which units should be used to express the answer according to proper dimensional analysis?

Accepted Answer

$$60\ 	ext{km/h}$$; units of speed are always length/time$

Question 2

Which of the following best describes the difference between speed and velocity?

Accepted Answer

Speed is a scalar quantity, while velocity is a vector quantity with both magnitude and direction.

Question 3

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

Accepted Answer

$$\vec{A} = 5\cos(53^\circ)\hat{i} + 5\sin(53^\circ)\hat{j}$$

Question 4

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 by the ball? (Assume $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$h = \frac{v_0$^2}{2g} = \frac{(10)^2$}{2 	imes 9.8} = 5.1\ 	ext{m}$$

Question 5

Which of the following statements about projectile motion on planet Earth is always true?

Accepted Answer

The horizontal acceleration is zero, and the vertical acceleration is $$-g.$$

Question 6

A vector $$\vec{B} is $$given as $$\vec{B} = 3\hat{i} + 4\hat{j}. $$What is the magnitude and direction (angle with respect to the x-axis) of $$\vec{B}$$?

Accepted Answer

Magnitude: $$5$$; Direction: $$	heta = \arctan\left(\frac{4}{3}ight) \approx 53^\circ$$

Question 7

A train accelerates from rest at $$2\ 	ext{m/s}^2$$ for $$5$$ seconds. What is its final velocity?

Accepted Answer

$$v = v_0$ + at = 0 + 2 	imes 5 = 10\ 	ext{m/s}$$

Question 8

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What is the time of flight before it lands back at the same height? (Neglect air resistance)

Accepted Answer

$$T = \frac{2v_0\sin	heta}{g}$$

Question 9

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

Accepted Answer

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

Question 10

A cyclist moves along a circular path of radius $$10\ 	ext{m} at a $$constant speed of $$5\ 	ext{m/s}. $$What is the period $$T of $$the motion?

Accepted Answer

$$T = \frac{2\pi r}{v} = \frac{2\pi 	imes 10}{5} = 4\pi \approx 12.6\ 	ext{s}$$

Question 11

A car moves east at $$20\ 	ext{m/s}$$ and then north at $$20\ 	ext{m/s}. $$What is the magnitude of its resultant velocity?

Accepted Answer

$$v = \sqrt{(20)^2$ + (20)^2$} = \sqrt{800} = 28.3\ 	ext{m/s}$$

Question 12

Which of the following is NOT a correct application of significant figures?

Accepted Answer

When multiplying $$2.5 (2 $$sig figs) by $$3.42 (3 $$sig figs), the answer should have 3 significant figures.

Question 13

A stone is dropped from a height of $$45\ 	ext{m}. $$How long does it take to reach 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 14

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 15

A projectile is launched horizontally from a $$20\ 	ext{m}$$ high cliff. How far from the base of the cliff does it land if its initial speed is $$15\ 	ext{m/s}$$? (Assume $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

Time to fall: $$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{40}{9.8}} \approx 2.02\ 	ext{s}$$; Range: $$x = v_0$ t = 15 	imes 2.02 \approx 30.3\ 	ext{m}$$

Question 16

Which equation correctly relates angular speed $$\omega to $$period $$T in $$uniform circular motion?

Accepted Answer

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

Question 17

A student converts $$5.0\ 	ext{m} to $$centimeters. Which is the correct conversion using dimensional analysis?

Accepted Answer

$$5.0\ 	ext{m} 	imes \frac{100\ 	ext{cm}}{1\ 	ext{m}} = 500\ 	ext{cm}$$

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

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