Q: A ball is thrown vertically upward with an initial velocity of $$15\ \mathrm{m/s}. $$Neglecting air resistance, what is the maximum height it reaches? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$h = \frac{v_0$^2}{2g} = \frac{(15)^2$}{2 \times 9.8} = 11.5\ \mathrm{m}$$

Q: A runner moves with a constant velocity of $$8\ \mathrm{m/s}$$ for $$10\ \mathrm{s}. $$What is the total displacement?

$$d = v t = 8 \times 10 = 80\ \mathrm{m}$$

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

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 45}{9.8}} = 3.03\ \mathrm{s}$$

Q: A car moves with a velocity given by $$v(t) = 3t^2$ where v$ is in $$\mathrm{m/s}$$ and t$ in $$\mathrm{s}$$. What is the instantaneous acceleration at t = 2$$\ \mathrm{s}$$?

$$a = \frac{dv}{dt} = 6t;\ a = 6 \times 2 = 12\ \mathrm{m/s^2$}$$

Q: A train travels at $$30\ \mathrm{m/s}$$ for $$2\ \mathrm{min}. $$How far does it travel?

$$d = v t = 30 \times 120 = 3600\ \mathrm{m}$$

Question 1

A car starts from rest and accelerates uniformly along a straight road. After 5 seconds, it reaches a velocity of 20 m/s. What is the magnitude of its acceleration?

Accepted Answer

$$a = \frac{20\ \mathrm{m/s}}{5\ \mathrm{s}} = 4\ \mathrm{m/s^2$}$$

Question 2

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

Accepted Answer

Displacement is the straight-line vector from initial to final position, while distance is the total path length traveled.

Question 3

A ball is thrown vertically upward with an initial velocity of $$15\ \mathrm{m/s}. $$Neglecting air resistance, what is the maximum height it reaches? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$h = \frac{v_0$^2}{2g} = \frac{(15)^2$}{2 	imes 9.8} = 11.5\ \mathrm{m}$$

Question 4

Which of the following is the correct SI unit for acceleration?

Accepted Answer

$$\mathrm{m/s^2$}$$

Question 5

A runner moves with a constant velocity of $$8\ \mathrm{m/s}$$ for $$10\ \mathrm{s}. $$What is the total displacement?

Accepted Answer

$$d = v t = 8 	imes 10 = 80\ \mathrm{m}$$

Question 6

Which of the following statements about instantaneous velocity is correct?

Accepted Answer

It is the derivative of position with respect to time.

Question 7

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

Accepted Answer

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

Question 8

Which of the following is NOT a vector quantity?

Accepted Answer

Distance

Question 9

A car travels east for $$100\ \mathrm{m}$$, then west for $$40\ \mathrm{m}. $$What is the total displacement?

Accepted Answer

$$60\ \mathrm{m}$$ east

Question 10

A block slides down a frictionless inclined plane making an angle $$	heta$$ with the horizontal. What is the acceleration of the block?

Accepted Answer

$$a = g \sin 	heta$$

Question 11

A cyclist accelerates from $$5\ \mathrm{m/s} to$$ $$15\ \mathrm{m/s} in$$ $$4\ \mathrm{s}. $$What is the average acceleration?

Accepted Answer

$$a = \frac{15 - 5}{4} = 2.5\ \mathrm{m/s^2$}$$

Question 12

Which of the following best describes uniform motion?

Accepted Answer

Motion with constant velocity

Question 13

A car moves with a velocity given by $$v(t) = 3t^2$ where v$ is in $$\mathrm{m/s}$$ and t$ in $$\mathrm{s}$$. What is the instantaneous acceleration at t = 2$$\ \mathrm{s}$$?

Accepted Answer

$$a = \frac{dv}{dt} = 6t;\ a = 6 	imes 2 = 12\ \mathrm{m/s^2$}$$

Question 14

A train travels at $$30\ \mathrm{m/s}$$ for $$2\ \mathrm{min}. $$How far does it travel?

Accepted Answer

$$d = v t = 30 	imes 120 = 3600\ \mathrm{m}$$

Question 15

Which of the following is the correct formula for average velocity?

Accepted Answer

$$v_{avg} = \frac{\Delta x}{\Delta t}$$

Question 16

A rock is thrown downward from a cliff with an initial velocity of $$10\ \mathrm{m/s}. $$How far does it fall in $$3\ \mathrm{s}$$? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$d = v_0$ t + \frac{1}{2} g t^2$ = 10 	imes 3 + 0.5 	imes 9.8 	imes 9 = 30 + 44.1 = 74.1\ \mathrm{m}$$

Question 17

Which of the following is a correct statement about significant digits?

Accepted Answer

The number of significant digits reflects the precision of a measurement.

Question 18

A car accelerates uniformly from rest to $$25\ \mathrm{m/s} in$$ $$10\ \mathrm{s}. $$What is the total distance covered?

Accepted Answer

$$d = \frac{1}{2} a t^2$ = \frac{1}{2} 	imes 2.5 	imes 100 = 125\ \mathrm{m}$$

Question 19

A ball rolls off a table with a horizontal velocity of $$2\ \mathrm{m/s}$$ from a height of $$1.25\ \mathrm{m}. $$How long does it take to hit the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 	imes 1.25}{9.8}} = 0.505\ \mathrm{s}$$

Kinematics: Motion Along a Straight Line

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