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

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

Q: A rock is thrown straight up with an initial velocity of $$15\ \mathrm{m/s}. $$How high does it rise before coming to rest momentarily? (Use $$g = 9.8\ \mathrm{m/s}^2)$$

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

Q: A car accelerates from rest at $$2\ \mathrm{m/s}^2$$ for 5 seconds. What is its final velocity?

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

Q: A car is moving at $$12.5\ \mathrm{m/s}$$ and can brake with a magnitude of $$5\ \mathrm{m/s}^2. $$What is the stopping distance?

$$d = \frac{(12.5)^2$}{2 \times 5} = 15.625\ \mathrm{m}$$

Question 1

A car is moving at 20 m/s and comes to a stop in 4 seconds with constant acceleration. What is the magnitude of its acceleration?

Accepted Answer

$$a = \frac{0 - 20}{4} = -5\ \mathrm{m/s}^2$$

Question 2

Which of the following statements about acceleration is correct?

Accepted Answer

Acceleration is the rate of change of velocity.

Question 3

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

Accepted Answer

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

Question 4

If a car's initial speed is doubled, how does its stopping distance change, assuming the same braking acceleration?

Accepted Answer

The stopping distance is quadrupled.

Question 5

Which kinematic equation would you use to find the final velocity of an object given its initial velocity, acceleration, and displacement, but not time?

Accepted Answer

$$v_f^2$ = v_i^2$ + 2a(x_f - x_i)$$

Question 6

A rock is thrown straight up with an initial velocity of $$15\ \mathrm{m/s}. $$How high does it rise before coming to rest momentarily? (Use $$g = 9.8\ \mathrm{m/s}^2)$$

Accepted Answer

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

Question 7

Which of the following best describes the motion of a ball and a feather dropped simultaneously in a vacuum?

Accepted Answer

Both land at the same time because there is no air resistance.

Question 8

On a position vs. time graph, what does an upward curvature indicate about the acceleration?

Accepted Answer

The acceleration is positive.

Question 9

A car accelerates from rest at $$2\ \mathrm{m/s}^2$$ for 5 seconds. What is its final velocity?

Accepted Answer

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

Question 10

A car is moving at $$12.5\ \mathrm{m/s}$$ and can brake with a magnitude of $$5\ \mathrm{m/s}^2. $$What is the stopping distance?

Accepted Answer

$$d = \frac{(12.5)^2$}{2 	imes 5} = 15.625\ \mathrm{m}$$

Question 11

Which of the following is true about the acceleration due to gravity near the surface of the Earth?

Accepted Answer

It is approximately $$9.8\ \mathrm{m/s}^2$$ for all objects.

Question 12

A car travels with a constant acceleration. Which equation gives its position as a function of time?

Accepted Answer

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

Question 13

A ball is thrown downward with an initial velocity of $$5\ \mathrm{m/s}$$ from a height of $$20\ \mathrm{m}. $$How long does it take to hit the ground? (Use $$g = 9.8\ \mathrm{m/s}^2)$$

Accepted Answer

$$t = \frac{-5 + \sqrt{5^2$ + 2 	imes 9.8 	imes 20}}{9.8} \approx 1.37\ \mathrm{s}$$

Question 14

Which of the following best describes the relationship between velocity and acceleration when an object is slowing down?

Accepted Answer

Velocity and acceleration are in opposite directions.

Question 15

A car moves with a constant velocity of $$10\ \mathrm{m/s}$$ for 3 seconds, then accelerates at $$2\ \mathrm{m/s}^2$$ for 4 seconds. What is its final velocity?

Accepted Answer

$$v = 10 + 2 	imes 4 = 18\ \mathrm{m/s}$$

Question 16

On an inclined plane, which component of gravity causes an object to accelerate down the slope?

Accepted Answer

$$mg \sin 	heta$$

Question 17

A car travels 100 m in 5 seconds with constant acceleration, starting from rest. What is its acceleration?

Accepted Answer

$$a = \frac{2 	imes 100}{5^2$} = 8\ \mathrm{m/s}^2$$

Question 18

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

Accepted Answer

$$x_f = x_i + a t$$

Question 19

A ball is thrown upward and returns to its starting point. Which of the following is true about its velocity and acceleration at the highest point?

Accepted Answer

Velocity is zero, acceleration is $$-g.$$

Kinematics in One Dimension: Acceleration, Motion with Constant Acceleration, and Free Fall

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