### Concept Items

#### 3.1 Acceleration

How can you use the definition of acceleration to explain the units in which acceleration is measured?

- Acceleration is the rate of change of velocity. Therefore, its unit is m/s
^{2}. - Acceleration is the rate of change of displacement. Therefore, its unit is m/s.
- Acceleration is the rate of change of velocity. Therefore, its unit is m
^{2}/s. - Acceleration is the rate of change of displacement. Therefore, its unit is m
^{2}/s.

- ${\text{m}}^{2}\text{/s}$
- ${\text{cm}}^{2}\text{/s}$
- ${\text{m/s}}^{2}$
- ${\text{cm/s}}^{2}$

- The car is accelerating because the magnitude as well as the direction of velocity is changing.
- The car is accelerating because the magnitude of velocity is changing.
- The car is accelerating because the direction of velocity is changing.
- The car is accelerating because neither the magnitude nor the direction of velocity is changing.

#### 3.2 Representing Acceleration with Equations and Graphs

A student calculated the final velocity of a train that decelerated from 30.5 m/s and got an answer of −43.34 m/s. Which of the following might indicate that he made a mistake in his calculation?

- The sign of the final velocity is wrong.
- The magnitude of the answer is too small.
- There are too few significant digits in the answer.
- The units in the initial velocity are incorrect.

Create your own kinematics problem. Then, create a flow chart showing the steps someone would need to take to solve the problem.

- Acceleration
- Distance
- Displacement
- Force

- $v={v}_{0}+at$
- $v={v}_{0}-at$
- ${v}^{2}={{v}_{0}}^{2}+at$
- ${v}^{2}={{v}_{0}}^{2}-at$

### Critical Thinking Items

#### 3.1 Acceleration

- (a) Push down on the accelerator and then (b) push down again on the accelerator a second time.
- (a) Push down on the accelerator and then (b) push down on the brakes.
- (a) Push down on the brakes and then (b) push down on the brakes a second time.
- (a) Push down on the brakes and then (b) push down on the accelerator.

- $-33.75\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$
- $-15.00\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$
- $15.00\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$
- $33.75\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$

#### 3.2 Representing Acceleration with Equations and Graphs

A student is asked to solve a problem:

An object falls from a height for 2.0 s, at which point it is still 60 m above the ground. What will be the velocity of the object when it hits the ground?

Which of the following provides the correct order of kinematic equations that can be used to solve the problem?

- First use ${v}^{2}={v}_{0}{}^{2}+2a(d-{d}_{0})\text{,}$ then use $v={v}_{0}+at.$
- First use $v={v}_{0}+at,$ then use ${v}^{2}={v}_{0}{}^{2}+2a(d-{d}_{0})\text{.}$
- First use $d={d}_{0}+{v}_{0}t+\frac{1}{2}a{t}^{2},$ then use $v={v}_{0}+at.$
- First use $v={v}_{0}+at,$ then use $d-{d}_{0}={v}_{0}t+\frac{1}{2}a{t}^{2}.$

Skydivers are affected by acceleration due to gravity and by air resistance. Eventually, they reach a speed where the force of gravity is almost equal to the force of air resistance. As they approach that point, their acceleration decreases in magnitude to near zero.

Part A. Describe the shape of the graph of the magnitude of the acceleration versus time for a falling skydiver.

Part B. Describe the shape of the graph of the magnitude of the velocity versus time for a falling skydiver.

Part C. Describe the shape of the graph of the magnitude of the displacement versus time for a falling skydiver.

- A Part A. Begins with a nonzero y-intercept with a downward slope that levels off at zero; Part B. Begins at zero with an upward slope that decreases in magnitude until the curve levels off; Part C. Begins at zero with an upward slope that increases in magnitude until it becomes a positive constant
- Part A. Begins with a nonzero y-intercept with an upward slope that levels off at zero; Part B. Begins at zero with an upward slope that decreases in magnitude until the curve levels off; Part C. Begins at zero with an upward slope that increases in magnitude until it becomes a positive constant
- Part A. Begins with a nonzero y-intercept with a downward slope that levels off at zero; Part B. Begins at zero with a downward slope that decreases in magnitude until the curve levels off; Part C. Begins at zero with an upward slope that increases in magnitude until it becomes a positive constant
- Part A. Begins with a nonzero y-intercept with an upward slope that levels off at zero; Part B. Begins at zero with a downward slope that decreases in magnitude until the curve levels off; Part C. Begins at zero with an upward slope that increases in magnitude until it becomes a positive constant

Which graph in the previous problem has a positive slope?

- Displacement versus time only
- Acceleration versus time and velocity versus time
- Velocity versus time and displacement versus time
- Acceleration versus time and displacement versus time

### Problems

#### 3.1 Acceleration

The driver of a sports car traveling at 10.0 m/s steps down hard on the accelerator for 5.0 s and the velocity increases to 30.0 m/s. What was the average acceleration of the car during the 5.0 s time interval?

- –1.0 × 102 m/s
^{2} - –4.0 m/s
^{2} - 4.0 m/s
^{2} - 1.0 × 102 m/s
^{2}

A girl rolls a basketball across a basketball court. The ball slowly decelerates at a rate of −0.20 m/s^{2}. If the initial velocity was 2.0 m/s and the ball rolled to a stop at 5.0 sec after 12:00 p.m., at what time did she start the ball rolling?

- 0.1 seconds before noon
- 0.1 seconds after noon
- 5 seconds before noon
- 5 seconds after noon

#### 3.2 Representing Acceleration with Equations and Graphs

A swan on a lake gets airborne by flapping its wings and running on top of the water. If the swan must reach a velocity of 6.00 m/s to take off and it accelerates from rest at an average rate of 0.350 m/s^{2}, how far will it travel before becoming airborne?

- −8.60 m
- 8.60 m
- −51.4 m
- 51.4 m

- $0.408\phantom{\rule{thinmathspace}{0ex}}\text{s}$
- $0.816\phantom{\rule{thinmathspace}{0ex}}\text{s}$
- $1.34\phantom{\rule{thinmathspace}{0ex}}\text{s}$
- $1.75\phantom{\rule{thinmathspace}{0ex}}\text{s}$
- 1.28 s

### Performance Task

#### 3.2 Representing Acceleration with Equations and Graphs

Design an experiment to measure displacement and elapsed time. Use the data to calculate final velocity, average velocity, acceleration, and acceleration.

- a small marble or ball bearing
- a garden hose
- a measuring tape
- a stopwatch or stopwatch software download
- a sloping driveway or lawn as long as the garden hose with a level area beyond

(a) How would you use the garden hose, stopwatch, marble, measuring tape, and slope to measure displacement and elapsed time? Hint—The marble is the accelerating object, and the length of the hose is total displacement.

(b) How would you use the displacement and time data to calculate velocity, average velocity, and acceleration? Which kinematic equations would you use?

(c) How would you use the materials, the measured and calculated data, and the flat area below the slope to determine the negative acceleration? What would you measure, and which kinematic equation would you use?