Q: If an object starts from rest and accelerates at $$2.0\ \mathrm{m/s}^2$$ for 4.0 seconds, what is its final velocity?

$$v = v_0$ + a t = 0 + 2.0 \times 4.0 = 8.0\ \mathrm{m/s}$$

Question 1

A car slows down from 15.0 m/s to 5.0 m/s in 3.0 seconds. What is the car's average acceleration during this time interval?

Accepted Answer

$$a_{avg} = \frac{5.0\ \mathrm{m/s} - 15.0\ \mathrm{m/s}}{3.0\ \mathrm{s}} = -3.33\ \mathrm{m/s}^2$$

Question 2

Which of the following best describes average acceleration?

Accepted Answer

The change in velocity divided by the time interval over which the change occurs.

Question 3

A runner increases her velocity from 2.0 m/s to 6.0 m/s in 2.0 seconds. What is her average acceleration?

Accepted Answer

$$a_{avg} = \frac{6.0\ \mathrm{m/s} - 2.0\ \mathrm{m/s}}{2.0\ \mathrm{s}} = 2.0\ \mathrm{m/s}^2$$

Question 4

If the velocity of a car is non-zero, can its acceleration be zero? Choose the best explanation.

Accepted Answer

Yes, if the car is moving at constant velocity, its acceleration is zero.

Question 5

A car is traveling at 30 m/s on wet pavement. The driver sees a stopped car ahead and has a reaction time of 0.75 s before applying the brakes. If the car decelerates at $$-5.0\ \mathrm{m/s}^2$$ after the brakes are applied, how far does the car travel from the moment the driver sees the stopped car until it comes to rest?

Accepted Answer

First, distance during reaction: $$d_1 = v t = 30$$\ \mathrm{m/s} 	imes 0.75\ \mathrm{s} = 22.5\ \mathrm{m}$$. Then, stopping distance: d_2$ = \frac{v^2$}{2|a|} = \frac{(30\ \mathrm{m/s})^2$}{2 	imes 5.0\ \mathrm{m/s}^2} = 90\ \mathrm{m}. $$Total distance: $$22.5\ \mathrm{m} + 90\ \mathrm{m} = 112.5\ \mathrm{m}.$$

Question 6

Which of the following equations is NOT valid for constant acceleration motion?

Accepted Answer

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

Question 7

A velocity vs. time graph for an object moving with constant acceleration is:

Accepted Answer

A straight line with a constant slope.

Question 8

If an object starts from rest and accelerates at $$2.0\ \mathrm{m/s}^2$$ for 4.0 seconds, what is its final velocity?

Accepted Answer

$$v = v_0$ + a t = 0 + 2.0 	imes 4.0 = 8.0\ \mathrm{m/s}$$

Question 9

A cyclist moves with a constant acceleration. Which of the following statements is true?

Accepted Answer

The velocity changes by equal amounts in equal time intervals.

Question 10

Which of the following is a correct problem-solving strategy for constant acceleration problems?

Accepted Answer

Draw a motion diagram or velocity vs. time graph to visualize the problem.

Question 11

A ball is thrown straight up with an initial velocity of $$20\ \mathrm{m/s}. $$What is its velocity after 2 seconds? (Assume $$a = -9.8\ \mathrm{m/s}^2)$$

Accepted Answer

$$v = v_0$ + a t = 20 + (-9.8) 	imes 2 = 0.4\ \mathrm{m/s}$$

Question 12

Which of the following best describes acceleration as a vector quantity?

Accepted Answer

It has both magnitude and direction.

Question 13

A car moves with a constant velocity of $$10\ \mathrm{m/s}$$ for 5 seconds. What is its acceleration?

Accepted Answer

$$a = 0\ \mathrm{m/s}^2$$

Question 14

A train starts from rest and accelerates uniformly at $$1.5\ \mathrm{m/s}^2$$ for 10 seconds. How far does it travel in this time?

Accepted Answer

$$x = x_0$ + v_0$ t + \frac{1}{2} a t^2$ = 0 + 0 + 0.5 	imes 1.5 	imes (10)^2$ = 75\ \mathrm{m}$$

Question 15

Which of the following is NOT a step in the recommended problem-solving strategy for constant acceleration problems?

Accepted Answer

Assume all quantities are positive.

Question 16

A car accelerates from rest at $$4.0\ \mathrm{m/s}^2. $$How long does it take to reach a speed of $$20\ \mathrm{m/s}$$?

Accepted Answer

$$t = \frac{v - v_0$}{a} = \frac{20 - 0}{4.0} = 5.0\ \mathrm{s}$$

Question 17

Which of the following real-life scenarios best illustrates the concept of negative acceleration?

Accepted Answer

A car coming to a stop at a red light.

Kinematics: Acceleration and Problem-Solving Strategies (Physics 101 Study Notes)

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