Q: A car travels 120 km in 2 hours. What is its average speed, and how does this differ from 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 student measures the length of a table as $$2.50\ \text{m}$$, $$2.5\ \text{m}$$, and $$2.500\ \text{m}. $$Which measurement has the greatest number of significant figures?

$$2.500\ \text{m}$$ has 4 significant figures.

Q: Convert $$5.0\ \text{m/s} to$$ $$\text{km/h}$$ using dimensional analysis.

$$5.0\ \text{m/s} \times \frac{3600\ \text{s}}{1\ \text{h}} \times \frac{1\ \text{km}}{1000\ \text{m}} = 18\ \text{km/h}$$

Q: A projectile is launched from ground level with an initial velocity of $$20\ \text{m/s} at an $$angle of $$45^\circ$$ above the horizontal. What is the time of flight before it lands back on the ground? (Assume $$g = 9.8\ \text{m/s}^2)$$

$$t = \frac{2v_0\sin\theta}{g} = \frac{2 \times 20 \times \sin 45^\circ}{9.8} \approx 2.9\ \text{s}$$

Q: A ball is thrown vertically upward with an initial velocity of $$15\ \text{m/s}. $$How high does it rise? (Assume $$g = 9.8\ \text{m/s}^2)$$

$$h = \frac{v_0$^2}{2g} = \frac{15^2$}{2 \times 9.8} \approx 11.5\ \text{m}$$

Q: A vector $$\vec{B} = 3\hat{i} + 4\hat{j} is $$given. What is its magnitude and direction relative to the x-axis?

Magnitude: $$\sqrt{3^2$ + 4^2$} = 5$$; Direction: $$\tan$$^{-1}$$(\frac{4}{3}) \approx 53^\circ$$

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

$$a_c = \frac{v^2$}{r} = \frac{5^2$}{10} = 2.5\ \text{m/s}^2$$

Question 1

A car travels 120 km in 2 hours. What is its average speed, and how does this differ from 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

A student measures the length of a table as $$2.50\ 	ext{m}$$, $$2.5\ 	ext{m}$$, and $$2.500\ 	ext{m}. $$Which measurement has the greatest number of significant figures?

Accepted Answer

$$2.500\ 	ext{m}$$ has 4 significant figures.

Question 3

Convert $$5.0\ 	ext{m/s} to$$ $$	ext{km/h}$$ using dimensional analysis.

Accepted Answer

$$5.0\ 	ext{m/s} 	imes \frac{3600\ 	ext{s}}{1\ 	ext{h}} 	imes \frac{1\ 	ext{km}}{1000\ 	ext{m}} = 18\ 	ext{km/h}$$

Question 4

A vector $$\vec{A}$$ has a magnitude of $$10$$ units and points $$30^\circ$$ above the positive x-axis. What is its unit vector form?

Accepted Answer

$$\vec{A} = 10\cos(30^\circ)\hat{i} + 10\sin(30^\circ)\hat{j}$$

Question 5

A projectile is launched from ground level with an initial velocity of $$20\ 	ext{m/s} at an $$angle of $$45^\circ$$ above the horizontal. What is the time of flight before it lands back on the ground? (Assume $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$t = \frac{2v_0\sin	heta}{g} = \frac{2 	imes 20 	imes \sin 45^\circ}{9.8} \approx 2.9\ 	ext{s}$$

Question 6

Which of the following statements about free fall is correct?

Accepted Answer

In free fall, the only force acting on the object is gravity, and acceleration is $$g$$ downward.

Question 7

A ball is thrown vertically upward with an initial velocity of $$15\ 	ext{m/s}. $$How high does it rise? (Assume $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$h = \frac{v_0$^2}{2g} = \frac{15^2$}{2 	imes 9.8} \approx 11.5\ 	ext{m}$$

Question 8

Which kinematic equation is best suited to find the final velocity of an object after traveling a known displacement with constant acceleration?

Accepted Answer

$$v^2$$ = $$v_0^2 + 2a$$\Delta x$$

Question 9

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

Accepted Answer

Magnitude: $$\sqrt{3^2$ + 4^2$} = 5$$; Direction: $$	an$$^{-1}$$(\frac{4}{3}) \approx 53^\circ$$

Question 10

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

Accepted Answer

$$a_c = \frac{v^2$}{r} = \frac{5^2$}{10} = 2.5\ 	ext{m/s}^2$$

Question 11

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

Accepted Answer

It always points toward the center of the circle.

Question 12

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

Accepted Answer

$$\Delta x = v_0$ t + \frac{1}{2} a t^2$ = 0 + \frac{1}{2} 	imes 2 	imes 5^2$ = 25\ 	ext{m}$$

Question 13

A projectile is launched horizontally from a $$20\ 	ext{m}$$ high cliff. How long does it take to hit the ground? (Assume $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{40}{9.8}} \approx 2.02\ 	ext{s}$$

Question 14

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 $$-g.$$

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 moves along a curved path and speeds up. Which type(s) of acceleration does it experience?

Accepted Answer

Both radial (centripetal) and tangential acceleration.

Question 17

A vector $$\vec{C} is$$ $$6\hat{i} - 8\hat{j}. $$What is its magnitude and direction relative to the x-axis?

Accepted Answer

Magnitude: $$\sqrt{6^2$ + (-8)^2$} = 10$$; Direction: $$	an$$^{-1}$$(\frac{-8}{6}) \approx -53^\circ$$

Question 18

A runner accelerates from $$2\ 	ext{m/s} to$$ $$6\ 	ext{m/s} in$$ $$4\ 	ext{s}. $$What is her average acceleration?

Accepted Answer

$$a_{avg} = \frac{v - v_0$}{t} = \frac{6 - 2}{4} = 1\ 	ext{m/s}^2$$

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

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