# Physics

**Hint 1. **Definition of average velocity

Average velocity is defined as the constant velocity at which an object would have to travel to achieve a given

displacement (difference between final and initial positions, which can be negative) over a given time interval,

from the initial time to the final time . The average velocity is therefore equal to the displacement divided

by the given time interval. In symbolic form, average velocity is given by

.

ANSWER:

Correct

Part B

Find the average velocity over the time interval from 1 to 3 seconds.

Express your answer in meters per second to the nearest integer.

**Hint 1. **Find the change in position

The final and initial positions can be read off the *y *axis of the graph. What is the displacement during the time

interval from 1 to 3 seconds?

Express your answer numerically, in meters

ANSWER:

**Hint 2. **Definition of average velocity

Average velocity is defined as the constant velocity at which an object would have to travel to achieve a given

displacement (difference between final and initial positions, which can be negative) over a given time interval,

from the initial time to the final time . The average velocity is therefore equal to the displacement divided

by the given time interval. In symbolic form, average velocity is given by

.

ANSWER:

0J 0G

2BWF<0J 0G >-

40G Ã40J

0G Ã0J

2BWF <> = 0 NT

4G Ã4J = 40 N

0J 0G

2BWF<0J 0G >-

40G Ã40J

0G Ã0J

11/10/2014 HW_Week2

http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2992507 9/29

Correct

A note about instantaneous velocity. The instantaneous velocity at a certain moment in time is represented by

the slope of the graph at that moment. For straightline

graphs, the (instantaneous) velocity remains constant

over the interval, so the instantaneous velocity at any time during an interval is the same as the average

velocity over that interval. For instance, in this case, the instantaneous velocity at any time from 1 to 3 seconds

is the same as the average velocity of .

Part C

Now find .

Give your answer to three significant figures.

**Hint 1. **A note on the displacement

Since the object’s position remains constant from time 0 to time 1, the object’s displacement from 0 to 3 is the

same as in Part B. However, the time interval has changed.

ANSWER:

Correct

Note that is not equal to the simple arithmetic average of and , i.e.,

, because they are averages for time intervals of different lengths.

Part D

Find the average velocity over the time interval from 3 to 6 seconds.

Express your answer to three significant figures.

**Hint 1. **Determine the displacement

What is the displacement?

Answer to the nearest integer.

ANSWER:

2BWF <> = 20 NT

NT

2BWF <>

2BWF <> = 13.3 NT

2BWF <> 2BWF <> 2BWF <>

2BWF<>2BWF<>

4 Ã4 = 40

N

11/10/2014 HW_Week2

http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2992507 10/29

**Hint 2. **Determine the time interval

What is the time interval?

Answer to two significant figures.

ANSWER:

ANSWER:

Correct

Part E

Finally, find the average velocity over the whole time interval shown in the graph.

Express your answer to three significant figures.

**Hint 1. **Determine the displacement

What is the displacement?

Answer to the nearest integer.

ANSWER:

ANSWER:

Correct

Note that though the *average *velocity is zero for this time interval, the *instantaneous *velocity (i.e., the slope of

the graph) has several different values (positive, negative, zero) during this time interval.

Note as well that since average velocity over a time interval is defined as the change in position (displacement)

in the given interval divided by the time, the object can travel a great distance (here 80 meters) and still have

zero average velocity, since it ended up exactly where it started. Therefore, zero average velocity does not

necessarily mean that the object was standing still the entire time!

Given Positions, Find Velocity and Acceleration

0G Ã0J = 3.0 T

2BWF <> = 13.3

NT

4 Ã4 = 0 N

2BWF <> = 0 NT

11/10/2014 HW_Week2

http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2992507 11/29

Learning Goal:

To understand how to graph position, velocity, and acceleration of an object starting with a table of positions vs. time.

The table shows the *x *coordinate of a moving object. The position is tabulated at 1s

intervals. The *x *coordinate is

indicated below each time. You should make the simplification that the acceleration of the object is bounded and

contains no spikes.

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?

**Hint 1. **Meaning of a bounded and nonspiky acceleration

A bounded and nonspiky acceleration results in a smooth graph of vs. .

ANSWER:

Correct

Part B

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

40

4 0

1

2

3

4

20