Lab 1. Representations of Linear Motion
Introduction
The following exercises present a simple description of an object’s motion in one form that you
are to translate into other, complementary forms or representations. The representations are: (1) a
word description, (2) a picture showing the position of the object at equally spaced time intervals
(like a picture taken with a strobe light), (3) a position-time graph (x versus t), (4) a velocity-time
graph (v versus t), and (5) an acceleration-time graph (a versus t).
Specific instructions
Given any one of these representations it is possible to complete all of the others. However, in
some cases there is more than one possibility for a particular representation. The important thing
is that each of your representations for any given case must be consistent with the others. In
other words all of the basic relationships between position, velocity, and acceleration that you
have learned must be satisfied for each case. (For example, velocity is the time rate of change of
position.)
1. In the “Word description of the motion”, provide a short, clear description of the motion by
the object.
2. In the “Strobe photograph”, indicate the starting point of the motion by an “S” inside a small
box and then show the subsequent positions at equally spaced time intervals. Be sure to
include the location of x = 0 (the origin) and show which direction is the positive x-direction.
An arrow to show the direction of the motion of the object is also necessary.
3. In the graphs, show the position, velocity, and acceleration (vertical axes) as functions of
time (horizontal axis). Make the time on all three of these graphs correspond as closely as
possible to the same scale: a special event on the position-time graph should appear at the
same point in time on the velocity-time and acceleration-time graphs.
4. Because this is a tutorial and not an official lab record, please use pencil.
The first case has been worked out in detail to illustrate the process.
Using this sheet as the cover page, staple all your completed worksheets together in numerical
order and submit them to the TA before leaving the lab. Make sure that your name, student ID
number, and lab section number are on the cover page.
1
Case 1
Word description of the motion:
Constant Positive Acceleration
x
Object starts at rest from the
origin and speeds up as it
travels in the positive “x”
direction away from the origin.
t
v
t
“Strobe” photograph:
S
x=0
a
t
Positive “x” direction
Case 2
Word description of the motion:
Constant Positive Position
x
t
v
t
“Strobe” photograph:
a
t
Case 3
Word description of the motion:
Constant Positive Velocity
x
t
v
t
“Strobe” photograph:
a
t
Case 4
Word description of the motion:
Constant Zero Position
x
t
v
t
“Strobe” photograph:
a
t
Case 5
Word description of the motion:
Constant Zero Velocity
x
t
v
t
“Strobe” photograph:
a
t
Case 6
Word description of the motion:
Constant Zero Acceleration
x
t
v
t
“Strobe” photograph:
a
t
Case 7
Word description of the motion:
Constant Negative Position
x
t
v
t
“Strobe” photograph
a
t
Case 8
Word description of the motion:
Constant Negative Velocity
x
t
v
t
“Strobe” photograph:
a
t
Case 9
Word description of the motion:
Constant Negative Acceleration
x
t
v
t
“Strobe” photograph:
a
t
Special Instructions for Cases 10, 11, and 12
The specifications for Cases 10, 11, and 12 are the same as for Cases 1, 6, and 9 respectively.
However, you are to find alternate solutions for Cases 10, 11, and 12, where both the position-time
and velocity-time graphs are significantly different from the solutions you previously gave for the
corresponding Cases 1, 6, and 9. For example, changing a positive value of accleration to a larger
positive value does not constitute a significant change in that quantity.
Case 10
Word description of the motion:
Constant Positive Acceleration
x
t
v
t
“Strobe” photograph:
a
t
Case 11
Word description of the motion:
Constant Zero Acceleration
x
t
v
t
“Strobe” photograph:
a
t
Case 12
Constant Negative Acceleration
Word description of the motion:
x
t
v
t
“Strobe” photograph:
a
t
Case 13
Word description of the motion:
At some position x > 0 the object is
traveling in the negative x-direction
and slowing down at a constant rate.
The object momentarily comes to
rest at some position x < 0. Immediately it
begins to speed up again at a constant
rate in the negative x-direction.
x
t
v
t
“Strobe” photograph:
a
t