Q: A ball is thrown vertically upward with an initial velocity of $$15\ \mathrm{m/s}. $$What is the maximum height reached by the ball? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

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

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

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

Q: A car travels $$100\ \mathrm{m} in$$ $$5\ \mathrm{s}$$ starting from rest with constant acceleration. What is the acceleration?

$$a = \frac{2s}{t^2$} = \frac{2 \times 100}{25} = 8\ \mathrm{m/s^2$}$$

Q: A runner accelerates from $$2\ \mathrm{m/s} to$$ $$8\ \mathrm{m/s} in$$ $$3\ \mathrm{s}. $$What is the displacement during this time?

$$s = \frac{(u + v)}{2} t = \frac{(2 + 8)}{2} \times 3 = 15\ \mathrm{m}$$

Q: A car moves with a velocity of $$10\ \mathrm{m/s}$$ for $$5\ \mathrm{s}$$ and then accelerates uniformly to $$20\ \mathrm{m/s} in $$the next $$5\ \mathrm{s}. $$What is the total distance covered?

$$s = 10 \times 5 + \frac{(10 + 20)}{2} \times 5 = 50 + 75 = 125\ \mathrm{m}$$

Question 1

A car accelerates uniformly from rest to a velocity of $$20\ \mathrm{m/s} in$$ $$10\ \mathrm{s}. $$What is the acceleration of the car?

Accepted Answer

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

Question 2

Which of the following equations correctly relates displacement $$s$$, initial velocity $$u$$, time $$t$$, and acceleration $$a$$ for uniformly accelerated motion?

Accepted Answer

$$s = ut + \frac{1}{2}at^2$

Question 3

A ball is thrown vertically upward with an initial velocity of $$15\ \mathrm{m/s}. $$What is the maximum height reached by the ball? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

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

Question 4

A train travels at $$30\ \mathrm{m/s}$$ and comes to rest in $$1\ \mathrm{min}$$ with uniform deceleration. What is the magnitude of its acceleration?

Accepted Answer

$$a = \frac{0 - 30}{60} = -0.5\ \mathrm{m/s^2$}$$

Question 5

Which of the following statements about velocity and acceleration is correct?

Accepted Answer

An object can have zero velocity and non-zero acceleration.

Question 6

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

Accepted Answer

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

Question 7

A cyclist increases her speed from $$5\ \mathrm{m/s} to$$ $$15\ \mathrm{m/s} in$$ $$5\ \mathrm{s}. $$What is her acceleration?

Accepted Answer

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

Question 8

Which of the following best describes the motion of an object with a constant negative acceleration?

Accepted Answer

Its velocity decreases linearly with time.

Question 9

A car travels $$100\ \mathrm{m} in$$ $$5\ \mathrm{s}$$ starting from rest with constant acceleration. What is the acceleration?

Accepted Answer

$$a = \frac{2s}{t^2$} = \frac{2 	imes 100}{25} = 8\ \mathrm{m/s^2$}$$

Question 10

A runner accelerates from $$2\ \mathrm{m/s} to$$ $$8\ \mathrm{m/s} in$$ $$3\ \mathrm{s}. $$What is the displacement during this time?

Accepted Answer

$$s = \frac{(u + v)}{2} t = \frac{(2 + 8)}{2} 	imes 3 = 15\ \mathrm{m}$$

Question 11

Which of the following is the correct unit for acceleration?

Accepted Answer

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

Question 12

A car moves with a velocity of $$10\ \mathrm{m/s}$$ for $$5\ \mathrm{s}$$ and then accelerates uniformly to $$20\ \mathrm{m/s} in $$the next $$5\ \mathrm{s}. $$What is the total distance covered?

Accepted Answer

$$s = 10 	imes 5 + \frac{(10 + 20)}{2} 	imes 5 = 50 + 75 = 125\ \mathrm{m}$$

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