Q: A ball is dropped from rest from the top of a 16 m tall building. Neglecting air resistance, how long does it take for the ball to hit the ground? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

$$t = \sqrt{\frac{2 \times 16}{9.8}}$$

Q: A car accelerates from rest at a constant rate of $$2\ \mathrm{m/s^2$}. $$How far does it travel in 5 seconds?

$$x = \frac{1}{2} a t^2$ = \frac{1}{2} \times 2 \times 5^2$ = 25\ \mathrm{m}$$

Q: A rock is thrown vertically upward with an initial velocity of $$10\ \mathrm{m/s}$$ from a height of $$16\ \mathrm{m}. $$What is the velocity of the rock just before it hits the ground? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{v_0$^2 + 2g x_0$} = \sqrt{10^2$ + 2 \times 9.8 \times 16}$$

Question 1

A ball is dropped from rest from the top of a 16 m tall building. Neglecting air resistance, how long does it take for the ball to hit the ground? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \sqrt{\frac{2 	imes 16}{9.8}}$$

Question 2

Which of the following equations gives the position $$x as a $$function of time $$t$$ for an object moving with constant acceleration $$a$$ and initial velocity $$v_0$$ from position $$x_0$$?

Accepted Answer

$$x = x_0$ + v_0$ t + \frac{1}{2} a t^2$

Question 3

A car accelerates from rest at a constant rate of $$2\ \mathrm{m/s^2$}. $$How far does it travel in 5 seconds?

Accepted Answer

$$x = \frac{1}{2} a t^2$ = \frac{1}{2} 	imes 2 	imes 5^2$ = 25\ \mathrm{m}$$

Question 4

Which of the following best describes the physical meaning of the area under an acceleration vs. time graph between $$t_1$$ and $$t_2$$?

Accepted Answer

It represents the change in velocity, $$\Delta v$$, during that time interval.

Question 5

A rock is thrown vertically upward with an initial velocity of $$10\ \mathrm{m/s}$$ from a height of $$16\ \mathrm{m}. $$What is the velocity of the rock just before it hits the ground? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{v_0$^2 + 2g x_0$} = \sqrt{10^2$ + 2 	imes 9.8 	imes 16}$$

Question 6

Which kinematic equation is most useful when the time variable is not given or required?

Accepted Answer

$$v^2$$ = $$v_0^2 + 2a(x$$ - $$x_0$$)$$

Question 7

A student claims that a heavier object falls faster than a lighter one in the absence of air resistance. Which scientist's experiments disproved this claim?

Accepted Answer

Galileo

Question 8

If the velocity of a particle is given by $$v(t) = 3t^2$, what is the acceleration as a function of time?

Accepted Answer

$$a(t) = \frac{dv}{dt} = 6t$$

Question 9

A ball is thrown straight up with velocity $$v_0$$ from ground level. What is the maximum height it reaches? (Neglect air resistance)

Accepted Answer

$$h_{max} = \frac{v_0$^2}{2g}$$

Question 10

Which of the following statements is true for an object in free fall near the Earth's surface (neglecting air resistance)?

Accepted Answer

The acceleration is constant and equal to $$-g.$$

Question 11

A car moves with constant acceleration. If its velocity increases from $$10\ \mathrm{m/s} to$$ $$30\ \mathrm{m/s} in$$ $$4\ \mathrm{s}$$, what is its acceleration?

Accepted Answer

$$a = \frac{v - v_0$}{t} = \frac{30 - 10}{4} = 5\ \mathrm{m/s^2$}$$

Question 12

The area under a velocity vs. time graph between $$t_1$$ and $$t_2$$ represents:

Accepted Answer

The displacement $$x - x_0$ during that time interval.

Question 13

A ball is thrown downward from a height of $$16\ \mathrm{m}$$ with an initial velocity of $$5\ \mathrm{m/s}. $$How long does it take to hit the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

Solve $$16 = 5t + \frac{1}{2} 9.8 t^2$

Question 14

Which of the following is the correct expression for average velocity $$v_{ave}$$ for constant acceleration?

Accepted Answer

$$v_{ave} = \frac{v_0$ + v}{2}$$

Question 15

A stone is dropped from rest from a cliff and falls for $$t$$ seconds. Which equation gives its velocity just before hitting the ground?

Accepted Answer

$$v = -g t$$

Question 16

If $$a(t) is a $$known function, which integral gives the velocity $$v(t)$$?

Accepted Answer

$$v(t) = v_0$ + \int_{0}^{t} a(t') dt'$$

Question 17

A ball is thrown upward with velocity $$v_0$$ from a height $$h. $$How long does it take to reach the maximum height?

Accepted Answer

$$t = \frac{v_0$}{g}$$

Question 18

Which of the following is NOT a valid kinematic equation for constant acceleration?

Accepted Answer

$$x = x_0$ + v t^2$

Motion in One Dimension: Velocity, Acceleration, and Freely Falling Bodies

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