Lab Section (circle):
Day:
Monday
Tuesday
Time: 8:00 9:30 1:10 2:40
Lab 1: One Dimensional Kinematics
Name:
Partners:
Pre-Lab
You are required to finish this section before coming to the lab, which will be checked by a lab
instructor when the lab begins.
Read your textbook and class notes on the theory about one-dimensional motion. Find the
definitions of the following: average speed, average velocity, speed, velocity, average acceleration,
and acceleration. Review the relationship between average velocity and velocity, and the relationship
between average acceleration and acceleration. Write down your pre-lab work below.
Note: displacement (or change in position), velocity, and acceleration are vector quantities, so
magnitude and direction for each must be specified to define the vector thoroughly. Directions for
any vector can be defined according to the context in which the vector is being analyzed; for
consistency in this lab, however, we are going to consider horizontal motion to be motion in the xdirection and vertical motion to be motion in the y-direction. Therefore, notation in this lab will
include, for example, x, vx and ax to represent the horizontal component, or x-component, of
position, velocity and acceleration respectively. y, vy, and ay will represent the corresponding
vertical components, or y-components, of these vectors.
I. Speed and Velocity
A. Average speed and average velocity.
Let's determine how fast you walk at your normal pace (no running is needed). Mark a starting
position and an ending position on the floor. The instruments you have are a tape measure and a stop
watch. Discuss as a group and decide what you will measure in order to find how fast you walk.
Then do the same measurements for each member in the group. Record the data measured for each
person. Since this is our first physics lab, we are providing the table below as an example for you to
organize your data.
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Based on your pre lab work, what should you enter in the fourth column to reflect how fast each
person walks? Write down the name of that quantity and the corresponding SI unit in the first cell of
the fourth column and fill in the other cells using your data.
NAME
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DISTANCE (M)
TIME (S)
a) For the first set of distance and time data, determine an appropriate uncertainty value for
each quantity and write each as best value ± uncertainty as described in the Introduction to
Experimental Uncertainty supplement on the Physics 107 Laboratory Handouts webpage.
b) For the first set of distance and time data, look at your calculated value in the fourth
column. Based on your response to (a), does your calculated value contain an appropriate
number of digits? Explain.
2) Is the quantity calculated above an accurate description of your motion within that time
interval?
3) If someone asks how fast you were moving 0.5 seconds before you stopped walking, could
you determine an answer based on your data?
4) What could you do to improve the description of your motion?
5) Is your average speed equal to your average velocity? State your reasoning.
B. Instantaneous Velocity
You are given a tape segment on your bench. The black dots on each segment represent the
successive positions of an object moving along a straight track. The position of the object is recorded
every 0.1 seconds.
1) Examine the tape segment. Describe the motion of the object.
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2) Using time, t, on the horizontal axis and position of the object, x, on the vertical axis, create a
graph representing the motion of the object. Select appropriate scales for the axes and label
them clearly..
a) What is the meaning of slope (i) in general mathematical terms (unrelated to position vs. time
graphs) and (ii) specifically for a position vs. time graph?
b) Describe how one finds the slope of a curved line at a certain instant. Assume you do not
know the equation for the line.
c) What is happening to the slope of the line in your graph as time progresses? What does this
tell you about the motion of the object?
d) What is a reasonable uncertainty for the measurements you made on the tape segment. What
physical factors contribute to the uncertainty?
Talk with an instructor before you continue.
II. Graphical Representations of Motion.
Now you use a motion detector to record data and to graph your motion. When using the motion
detector, stay in line with the detector and hold a large board (e.g., your lab folder) in front of you to
present a large target for the detector. For best results, do not get too close (< 0.15 meter) or too far
away (>5.0 m).
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1) The time interval between two data points recorded by the motion detector is 0.2 s or less,
much shorter than that in part 1A. Why does this make the data from the motion detector a
better description of a motion?
In the following graphs, we will use x, vx and ax to represent the horizontal components of
position, velocity and time as described in the pre-lab. t represents time. In each case, you are given
one piece of information of the motion. It is your job to predict the remaining three pieces of
information, and then check your prediction with the motion detector.
A. The x vs. t graph is given as shown.
xX (m)
Give a description of the motion in words.
(
4
0
t (s)
Using the axis below, sketch what the vx vs t and ax vs t graphs will look like for this motion. Label
the axes with appropriate units.
vx
ax
t
t
Use the motion detector to produce the given motion and to check your prediction. Draw what you
obtain below. (Note: Your graphs should emphasize important features, so draw them in an idealized
form rather than showing many wiggles.)
x
vx
ax
t
t
4
t
2) With reference to the motion detector’s surface, (a) what is the physical location
corresponding to the origin of the position graph? (b) What would you need to do to create a
graph with a constant positive slope?
B. The word description of the motion is given.
Description:
Starting walking toward the motion detector with constant velocity. Approximately
0.50 meter from the detector, change direction and move away from the detector at
the same speed. Stop at your original starting position.
Using the axis below, sketch what x vs. t, vx vs. t. and ax vs. t graphs will look like for this motion.
Label the axes with appropriate units.
x
vx
ax
t
t
t
3) Is the acceleration constant during the entire motion?
Use the motion detector to produce the given motion and to check your prediction. Draw what you
obtain from the motion detector below.
x
vx
ax
t
t
5
t
C. The word description of the motion is given.
Description:
Move toward the detector at a decreasing speed and stop approximately 0.50 meter
from the detector.
Using the axis below, sketch what x vs. t, vx vs. t. and ax vs. t graphs will look like for this motion.
Label the axes with appropriate units.
x
vx
ax
t
t
t
Use the motion detector to produce the given motion and to check your prediction. Draw what you
obtain from the motion detector below.
x
vx
ax
t
t
t
4) A toy car with remote control moves at constant velocity along a straight track until the
end of the track, then reverses its direction of motion at the same speed. The entire trip takes
place in the time span of 20 s. Which of the following two graphs is closer to the real situation?
State your reasoning.
a)
vxx
t
vxx
t
Talk with an instructor before you leave the lab.
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Homework Problems
Problem #1 For each of the following situations, assume that the positive direction is forwards and
negative is backwards.
Circle the appropriate response for questions a-d.
a) An object has positive velocity and positive acceleration.
i) The object is
speeding up
slowing down.
ii) The object is moving
forwards
backwards.
b) An object has negative velocity and positive acceleration.
i) The object is
speeding up
slowing down.
ii) The object is moving
forwards
backwards.
c) An object has negative velocity and negative acceleration.
i) The object is
speeding up
slowing down.
ii) The object is moving
forwards
backwards.
d) An object has positive velocity and negative acceleration.
i) The object is
speeding up
slowing down.
ii) The object is moving
forwards
backwards.
e) Use the graph below to answer the questions that follow.
Position
B
A
C
D
E
Time
i) During which segment(s) (A-F) is the object moving forwards?
ii) During which segment(s) does the object have negative velocity?
iii) During which segment(s) does the object have positive acceleration?
iv) During which segment(s) does the object have negative acceleration?
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F
Problem #2: The vy-vs-time graph below describes the vertical motion of a toy rocket, beginning
immediately when it is shot from the ground vertically up into the air. Neglect air resistance
when considering your responses.
vy
X
Y
0
Z
A
B
C
D
Time
a) At what point (X, Y, or Z) does the rocket reach its highest altitude?
b) During which segments (A, B, C and/or D) are vy positive?
c) During which segments (A, B, C and/or D) are ay positive?
d) At what point (X, Y, or Z) does the rocket run out of fuel?
e) What is the slope of line segment XZ (be as specific as possible)? Why?
f) What is happening to the rocket during segment D? What is the significance of the steep slope
of the line segment?
Problem #3: For each of the following ball and track configurations below,
i) Sketch x vs. t, vx vs. t and ax vs. t graphs, and
ii) For each different segment of the tracks, state the sign (+ or -) of both vx and ax and
comment on their effects on the motion of the ball (i.e. does it speed up or slow down).
For each configuration, assume x = 0 on the left side of each track and positive positions are to
the right. Neglect frictional effects.
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A. The ball rolls to the right from the left side of a level track segment and up an inclined segment.
It turns around and returns to its starting position.
x
ax
vx
t
t
9
t
B. A ball rolls back and forth on a pair of inclined tracks. Sketch the graph for one complete cycle.
x
ax
vx
t
t
10
t
Problem 4:
The following questions refer to obtaining information from postion and velocity vs time graphs.
Answer each with a thorough description. If it is impossible to find the information asked for, state
so explicitly.
A. How do you determine the direction an object is traveling from an x vs t graph? A vx vs t graph?
B. How do you determine the the location of an object at a particular instant in time from an x vs t
graph? A vx vs t graph?
C. How do you determine if an object is speeding up from an x vs t graph? A vx vs t graph?
D. How do you determine how fast an object is traveling from an x vs t graph? A vx vs t graph?
E. How do you determine if or whan an object changes direction from an x vs t graph? A vx vs t
graph?
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