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? Use $$g = 9.8\ \mathrm{m/s^2$}.$$

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

Q: A car accelerates from rest at a constant rate of $$2\ \mathrm{m/s^2$}. $$What is its velocity after 5 seconds?

$$v = 2 \times 5 = 10\ \mathrm{m/s}$$

Q: A rock is thrown straight upward from the edge of a 16 m high cliff with an initial velocity of $$10\ \mathrm{m/s}. $$How fast is it moving when it hits the ground below? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{(10)^2$ + 2 \times 9.8 \times 16}$$

Q: A student drops a ball from a height of 16 m. If the acceleration due to gravity on the Moon is $$1.6\ \mathrm{m/s^2$}$$, how long does it take to hit the ground?

$$t = \sqrt{\frac{2 \times 16}{1.6}}$$

Q: A car starts from rest and accelerates uniformly at $$3\ \mathrm{m/s^2$}$$ for 4 seconds. What is the total distance traveled?

$$x = \frac{1}{2} \times 3 \times 4^2$ = 24\ \mathrm{m}$$

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? Use $$g = 9.8\ \mathrm{m/s^2$}.$$

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 $$2\ \mathrm{m/s^2$}. $$What is its velocity after 5 seconds?

Accepted Answer

$$v = 2 	imes 5 = 10\ \mathrm{m/s}$$

Question 4

The area under the acceleration vs. time graph between $$t_1$$ and $$t_2$$ represents:

Accepted Answer

The change in velocity $$\Delta v$$ during $$t_1 to$$ $$t_2$$

Question 5

A rock is thrown straight upward from the edge of a 16 m high cliff with an initial velocity of $$10\ \mathrm{m/s}. $$How fast is it moving when it hits the ground below? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{(10)^2$ + 2 	imes 9.8 	imes 16}$$

Question 6

Which of the following is true about the average velocity for motion with constant acceleration?

Accepted Answer

It is the algebraic average of the initial and final velocities.

Question 7

If the velocity of an object is given by $$v(t) = v_0$ + at$$, what is the displacement after time $$t$$?

Accepted Answer

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

Question 8

A student drops a ball from a height of 16 m. If the acceleration due to gravity on the Moon is $$1.6\ \mathrm{m/s^2$}$$, how long does it take to hit the ground?

Accepted Answer

$$t = \sqrt{\frac{2 	imes 16}{1.6}}$$

Question 9

Which equation would you use to solve for the final velocity of an object when you know the initial velocity, acceleration, and displacement, but not the time?

Accepted Answer

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

Question 10

A car starts from rest and accelerates uniformly at $$3\ \mathrm{m/s^2$}$$ for 4 seconds. What is the total distance traveled?

Accepted Answer

$$x = \frac{1}{2} 	imes 3 	imes 4^2$ = 24\ \mathrm{m}$$

Question 11

Which of the following statements is correct regarding freely falling bodies (neglecting air resistance)?

Accepted Answer

All objects fall with the same constant acceleration regardless of their mass.

Question 12

A ball is thrown upward with an initial velocity of $$10\ \mathrm{m/s}. $$How long does it take to reach its maximum height? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \frac{10}{9.8}$$

Question 13

The slope of a velocity vs. time graph represents:

Accepted Answer

Acceleration

Question 14

If an object starts at $$x_0 = 0$ with v_0$ = 5\ \mathrm{m/s}$$ and $$a = 2\ \mathrm{m/s^2$}$$, what is its position after 3 seconds?

Accepted Answer

$$x = 0 + 5 	imes 3 + \frac{1}{2} 	imes 2 	imes 3^2$ = 24\ \mathrm{m}$$

Question 15

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

Accepted Answer

$$t = \frac{-5 + \sqrt{5^2$ + 2 	imes 9.8 	imes 16}}{9.8}$$

Question 16

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

Accepted Answer

$$x = x_0$ + a t$$

Question 17

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

Accepted Answer

The displacement $$x - x_0$ during t_1$ to t_2$

Question 18

A ball is thrown upward from the ground with $$v_0 = 15$$\ \mathrm{m/s}$$. How high does it rise before coming to rest momentarily? (g = 9.8$$\ \mathrm{$$m/s^2$$}$$)

Accepted Answer

$$h = \frac{(15)^2$}{2 	imes 9.8}$$

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

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