Mastering Physics 2

HOMEWORK1

Due: 11:00pm on Sunday, October 28, 2012

Note: You will receive no credit for late submissions. To learn more, read your instructor's GradingPolicy

Given Positions, Find Velocity and Acceleration

Learning Goal:

To graph position, velocity, and acceleration of an object given a table of positions vs. time.

The table below shows the x coordinate of a moving object. The position is tabulated at one-secondintervals. The x coordinate is indicated below each time.

time (s) 0 1 2 3 4 5 6 7 8 9

x (m) 0 1 4 9 16 24 32 40 46 48

Part A

Which graph best represents the function , describing the object's position vs.

time?

ANSWER:

Correct

Part B

Which of the following graphs best represents the function , describing the object's velocity as a

function of time?

1

2

3

4

Hint 1. Find the velocity toward the end of the motion

The velocity is given by the slope of the displacement (position) curve. Using this fact, thevelocity toward the end of the motion is __________.

Hint 1. Finding the slope

The slope of a displacement versus time curve is given by the equation

.

ANSWER:

Hint 2. Identify the implications of zero velocity

Two of the possible velocity vs. time graphs indicate zero velocity between and .

What would the corresponding position vs. time graph look like in this region?

ANSWER:

positive and increasing

positive and decreasing

negative and increasing

negative and decreasing

a horizontal line

straight but sloping up to the right

straight but sloping down to the right

curved upward

curved downward

ANSWER:

Correct

In principle, you could also compute and plot the average velocity. The expression for the averagevelocity is

.

The notation emphasizes that this is not an instantaneous velocity, but rather an

average over an interval from to . After you compute this, you must put a single point on the

graph of velocity vs. time. The most accurate place to plot the average velocity is at the middle ofthe time interval over which the average was computed.

Part C

Which of the following graphs bestrepresents the function , describing the

acceleration of this object?

Hint 1. Find the acceleration toward the end of the motion

The acceleration is given by the slope of the velocity curve. Toward the end of the motion, whenthe velocity is decreasing, the acceleration must be __________.

Hint 1. Finding the slope

The slope of a displacement versus time curve is given by the equation

1

2

3

4

.

ANSWER:

Hint 2. Calculate the acceleration in the region of constant velocity

What is the acceleration over the interval during which the object travels at constant speed?

Express your answer numerically in meters per second per second.

ANSWER:

ANSWER:

Correct

In one dimension, a linear increase or decrease in the velocity of an object over a given timeinterval implies constant acceleration over that particular time interval. You can find the magnitudeof the acceleration using the formula for average acceleration over a time interval:

.

When the acceleration is constant over an extended interval, you can choose any value of and

within the interval to compute the average.

Problem 2.32

A person driving her car at 45 approaches an intersection just as the traffic light turns yellow. She

knows that the yellow light lasts only 2.0 before turning red, and she is 28 away from the near side of

the intersection (see the figure).

zero

positive

negative

= 0

1

2

3

4

Part A

Should she try to stop, or should she speed up to cross the intersection before the light turns red? The

intersection is 15 wide. Her car's maximum deceleration is -5.8 , whereas it can accelerate

from 45 to 65 in 6.0 . Ignore the length of her car and her reaction time.

ANSWER:

Correct

Problem 2.44

A falling stone takes 0.28 to travel past a window 2.2 tall (see the figure).

She should stop.

She should speed up.

Part A

From what height above the top of the window did the stone fall?

Express your answer using two significant figures.

ANSWER:

All attempts used; correct answer displayed

Problem 2.56

The figure is a position versus time graph for themotion of an object along the axis.

Consider the time interval from A to B.

Part A

Is the object moving in the positive or negative direction?

ANSWER:

Correct

Part B

Is the object speeding up or slowing down?

ANSWER:

= 2.1

in the positive direction

in the negative direction

Correct

Part C

Is the acceleration of the object positive or negative?

ANSWER:

Correct

Now consider the time interval from D to E.

Part D

Is the object moving in the positive or negative direction?

ANSWER:

Correct

Part E

Is the object speeding up or slowing down?

ANSWER:

speeding up

slowing down

negative

positive

in the positive direction

in the negative direction

speeding up

slowing down

Correct

Part F

Is the acceleration of the object positive or negative?

ANSWER:

Correct

Part G

Finally, answer these same three questions for the time interval from C to D.

ANSWER:

Submitted, grade pending

Problem 2.5

A rolling ball moves from = 3.2 to = -4.8 during the time from = 3.2 to = 7.0 .

Part A

What is its average velocity?


ANSWER:

positive

negative

3693 Character(s) remaining

In the time interval from C to D; the object is not moving.In fact, the acceleration of the object is zero.

= -2.1

Correct

Problem 2.7

You are driving home from school steadily at 93 for 150 . It then begins to rain and you slow to 65

. You arrive home after driving 3 hours and 40 minutes.

Part A

How far is your hometown from school?


ANSWER:

Correct

Part B

What was your average speed?


ANSWER:

Correct

Problem 2.15

A bowling ball traveling with constant speed hits the pins at the end of a bowling lane 16.5 long. The

bowler hears the sound of the ball hitting the pins 2.40 after the ball is released from his hands.

Part A

What is the speed of the ball? The speed of sound is 340 .

ANSWER:

= 280

= 77

Correct

Problem 2.47

A stone is thrown vertically upward with a speed of 12.8 from the edge of a cliff 65.4 high (see the

figure).

Part A

How much later does it reach the bottom of the cliff?

ANSWER:

Answer Requested

Part B

What is its speed just before hitting?

ANSWER:

Answer Requested

= 7.02

= 5.19

= 38.0

Part C

What total distance did it travel?

ANSWER:

Correct

Problem 2.69

A stone is dropped from the roof of a high building. A second stone is dropped 1.94 later.

Part A

How far apart are the stones when the second one has reached a speed of 10.1 ?

ANSWER:

Answer Requested

Problem 2.81

A fast-food restaurant uses a conveyor belt to send the burgers through a grilling machine.

Part A

If the grilling machine is 1.4 long and the burgers require 2.1 to cook, how fast must the

conveyor belt travel?


ANSWER:

Correct

Part B

= 82.1

= 38.0

= 0.67

If the burgers are spaced 17 apart, what is the rate of burger production (in )?


ANSWER:

Correct

Score Summary:

Your score on this assignment is 65.8%.You received 65.83 out of a possible total of 100 points.

3.9

Mastering Physics 2

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