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Homework assignment 2 (covers Sections 2.1, 2.2, 2.3, 2.4, 2.5, 2.6)
Due: 2:00am on Monday, April 12, 2010
Note:
You will receive no credit for late submissions.
To learn more, read your instructor's
Grading Policy
First review Sections 2.1, 2.2, 2.3, 2.4, 2.5, and 2.6 of Young and Freedman,
including
the worked examples. You should then be able
to solve the problems given below.
Note
that you are allowed only 6 answer attempts per problem.
Given Positions, Find Velocity and Acceleration
Description:
Given a table of position versus time, identify graphs of an object's trajectory, velocity, and acceleration.
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 1-s 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 A.1
Meaning of a bounded and nonspiky acceleration
A bounded and nonspiky acceleration results in a smooth graph of
vs.
.
ANSWER:
1
2
3
4
Part B
Which of the following graphs best represents the function
,
describing the object's velocity as a function of time?
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MasteringPhysics
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Hint B.1
Find the velocity toward the end of the motion
Velocity is the time derivative of displacement. Given this, the velocity toward the end of the motion is __________.
ANSWER:
positive and increasing
positive and decreasing
negative and increasing
negative and decreasing
This narrows the options down to either graph 1 or 4.
Hint B.2
What are 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:
a horizontal line
straight but sloping up to the right
straight but sloping down to the right
curved upward
curved downward
So graphs 1 and 2 are incorrect.
Hint B.3
Specify the characteristics of the velocity function
The problem states that "the acceleration of the object is bounded and contains no spikes." This means that the velocity
___________.
ANSWER:
has spikes
has no discontinuities
has no abrupt changes of slope
is constant
Which graph or graphs satisfy this condition?
ANSWER:
1
2
3
4
In principle, you could also just compute and plot the average velocity. The expression for the average velocity is
.
The notation

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