Question 1

Which of the following equations describes the position $$x(t) of an $$object moving with constant acceleration $$a$$ and initial velocity $$v_0$$ from initial position $$x_0$$?

Accepted Answer

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

Question 2

An object is thrown straight up with an initial velocity of $$10\ \mathrm{m/s}. $$Neglecting air resistance, what is the acceleration of the object at the top of its path?

Accepted Answer

$$-9.8\ \mathrm{m/s^2$}$$\ downward

Question 3

Refer to the first set of plots in the first image. What is the sign of the acceleration, and how does the velocity change over time?

Accepted Answer

Acceleration is positive; velocity increases linearly.

Question 4

A ball is dropped from rest from a height of $$20\ \mathrm{m}. $$What is the velocity of the ball just before it hits the ground? (Assume $$g = 9.8\ \mathrm{m/s^2$}$$ and downward is negative.)

Accepted Answer

$$-14.0\ \mathrm{m/s}$$

Question 5

Which kinematic equation would you use to solve for the time it takes an object to fall a certain distance when dropped from rest?

Accepted Answer

$$x_f = x_i + v_i t + \frac{1}{2} a t^2$

Question 6

In the second set of plots in the first image, what is the direction of the acceleration and how does the position change over time?

Accepted Answer

Acceleration is negative; position decreases in a parabolic fashion.

Question 7

In the vacuum tube experiment shown in the second image, why do the apple and feather fall at the same rate?

Accepted Answer

Because there is no air resistance in the vacuum.

Question 8

If an object moves with constant velocity, what can you say about its acceleration and the shape of its position vs. time graph?

Accepted Answer

Acceleration is zero; position vs. time is a straight line.

Question 9

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

Accepted Answer

$$10\ \mathrm{m/s}$$

Question 10

A rock is thrown downward with an initial velocity of $$5\ \mathrm{m/s}$$ from a cliff $$30\ \mathrm{m}$$ high. What is its velocity just before hitting the ground? (Take $$g = 9.8\ \mathrm{m/s^2$}$$ downward.)

Accepted Answer

$$-27.2\ \mathrm{m/s}$$

Question 11

Which of the following statements about free fall is correct?

Accepted Answer

All objects in free fall accelerate at the same rate near Earth's surface, regardless of mass.

Question 12

A ball is thrown upward with an initial velocity $$v_0. At $$the highest point, which of the following is true?

Accepted Answer

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

Question 13

A car travels at a constant velocity of $$15\ \mathrm{m/s}$$ for $$10$$ seconds. How far does it travel?

Accepted Answer

$$150\ \mathrm{m}$$

Question 14

Which equation would you use to find the final velocity of an object given its initial velocity, acceleration, and displacement?

Accepted Answer

$$v_f^2$ = v_i^2$ + 2 a \Delta x$$

Question 15

A student drops a feather and a coin in a vacuum. What will happen?

Accepted Answer

Both will hit the ground at the same time.

Question 16

If $$a = 0$$, what is the general form of the position function $$x(t)$$?

Accepted Answer

$$x(t) = x_0$ + v_0$ t$$

Question 17

A runner accelerates from $$2\ \mathrm{m/s} to$$ $$8\ \mathrm{m/s} in$$ $$3$$ seconds. What is the average acceleration?

Accepted Answer

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

Question 18

Which of the following best describes the velocity vs. time graph for an object in free fall (neglecting air resistance)?

Accepted Answer

A straight line with negative slope.

Question 19

A ball is thrown straight up with velocity $$15\ \mathrm{m/s}. $$How long does it take to return to the thrower's hand? (Assume $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$3.06\ \mathrm{s}$$

Motion with Constant Acceleration and Free Fall

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