Kinematics
Kinematics
Speeding up
Important terms
Position
Slowing down
Velocity
Constant motion
Introduction
The purpose of this experiment is to to learn how to use a motion detector to measure motion, to
learn how to interpret graphs of position and velocity versus time and to understand the value of
measurement tools versus human guided tools (stopwatches, etc).
We describe the motion of an object by specifying its position, velocity, and acceleration. In this
experiment you will generate and interpret graphs of position vs. time and velocity vs. time. The
graphs will be generated by a cart moving on an air track and by a moving human, you or your
partner.
PRIOR TO LAB: Sketch a graph of position versus time that shows your body walking across a
room at a constant pace. Label the graph in your lab notebook. At the end of lab, come back to
your sketch to see how accurate you were in designing the graph.
x vs. t graphs for constant velocity
Velocity is distance over time or v = x/t. The slope of a graph is rise over run; hence, if the
graph is x vs. t then the slope, rise over run, is x/t, or velocity. Graphs of x vs. t are sketched
below, where x0 is the position of the object at t = 0.
v = x/t
= + const.
x
x
x0
0
v = x/t
= 0/t = 0
t
x
x0
0
x
x0
t
v = x/t
= - const.
x
t
t
0
t
In math books, graphs are often y vs. x, where y is plotted vertically, x is plotted horizontally, and
the equation of the straight line is
y = b + mx
where b is the vertical intercept, the value of y at x = 0, and m is the slope, the rise over run. For
the above graphs of x vs. t, the vertical intercept is x0 and the slope is v, hence the equation of
physics, analogous to the above math equation is:
x = x0 + vt
v vs. t graphs for constant acceleration
Acceleration, a, is change in velocity over time, a = v/t, hence acceleration is the slope of
v vs. t graphs, as shown below.
a = v/t
= + const.
v
v
v0
v
a = v/t
= 0/t = 0
0
v
v0
v0
v
t
t
0
t
a = v/t
= - const.
0
t
t
The general equation for v vs. t graphs is
v = v0 + at
where v0, velocity at t = 0, is the vertical intercept and a, the acceleration, is the slope.
x vs. t graphs for constant acceleration
Position vs. time graphs for constant acceleration are shown below.
x
x



t1

t2
t
t3
t4
t
The instantaneous velocity v at any time t is the slope of the tangent line, the dashed lines in the
graphs. For the left graph tangent lines are drawn at times t1 and t2. Note that the slope is
positive, v > 0, and increasing with time, thus the object is “speeding up” or accelerating. For the
right graph the slope is negative, v < 0, and decreasing, hence the object is “slowing down” or
decelerating.
Objectives



To explore how various motions are represented on a position-time graph.
To explore how various motions are represented on a velocity-time graph.
To discover the relationship between position-time and velocity-time graphs.
Motion Sensor
In this experiment a cart will move back and forth in front of a motion sensor. The motion
sensor will record the cart’s position as a function of time and display the graph on the computer.
Setup and Alignment
Computer Setup
1. Connect the Data Studio interface to the computer, turn on the interface, and then turn on the
computer.
2. Double click on the Data Studio icon. When the window opens click on Create Experiment.
3. Connect the motion sensor’s plugs to Digital Channels 1 and 2 of the Data Studio interface.
Connect the yellow plug to Digital Channel 1 and the black one to Digital Channel 2.
4. In the Sensors panel on the left, scroll down to Motion Sensor and double click. An icon for
the motion sensor will appear in the right panel. Double click on this icon and then select the
Motion Sensor tab. Change the trigger rate to 40 Hz. Do not click OK.
Alignment of Motion Sensor and Flag
1. With the air track blower turned off, bring the cart and Motion Sensor close together and
raise or lower the Motion Sensor until it is centered on the flag.
2. Position the flag at various distances, e.g., 0.5, 1.0, 1.5, and 2.0 m, and hence verify that the
Current Distance in each case is read to within 10 %. The system is ready to record motion.
Now click OK.
3. Double click on Graph in the Display panel in the lower left of the screen. Select Position as
the data source.
The Motion Sensor detects motion by sending and receiving sound waves. The received waves
for the motion of the cart on the air track are those that reflect off the flag on the cart. Make sure
objects are not near the track, which could act as reflectors, e.g., your body.
Flag
Bumper
Bumper
Motion
Sensor
Air track
Interface
Digital Analog
Computer
Recording Motion
2. With the cart near the Motion Sensor end of track, give it a shove. Click the Start button at
the top of the screen to start recording. Click the STOP button just before the cart reaches the
other end of the track.
3. Obtain a Velocity vs. Time graph by again double clicking on Graph in the display panel and
this time select “velocity”.
4. Obtain an Acceleration vs. Time graph by again double clicking on Graph in the display
panel and this time select “acceleration”.
Go through the attached conditions and sketch your prediction for the position, velocity, and
acceleration curves for each stated condition. You will first make predictions and then observe
the actual curves on your computer and skecth the results on the axis provided. Copy or paste
both your preditions and your results into your lab notebook. In order to provide a constant force
you may hang a weight from a pulley and attach it to your cart or tilt the track at an angle. Both
will work.
Refer to your experimental graphs to answer the following questions:
Question 1. What is the relationship between position, velocity, and acceleration?
Question 2. When is acceleration positive? When is it negative?
Question 3. When are the velocity and acceleration both the same sign? When are they opposite
signs?
Position
t
Position
t
Velocity
t
Velocity
t
t
Acceleration
Experiment: Cart moving away at constant v
Acceleration
Predition: Cart moving away at constant v
t
Position
t
Position
t
Velocity
t
Velocity
t
t
Acceleration
Experiment: Cart moving away and speeding up
Acceleration
Predition: Cart moving away and speeding up
t
Position
t
Position
t
Velocity
t
Velocity
t
t
Acceleration
Experiment:Cart moving away and slowing down
Acceleration
Predition: Cart moving away and slowing down
t
For the next two sets of graphs creat your own senario. Describe the experiment and compare
your predictions to your results.
Position
t
Position
t
Velocity
t
Velocity
t
t
Acceleration
Experiment:
Acceleration
Predition:
t
Position
t
Position
t
Velocity
t
Velocity
t
t
Acceleration
Experiment:
Acceleration
Predition:
t
Curve Fitting
Record both a position vs. time graph and a velocity vs. time graph for the cart travelling down
the track, rebounding, and returning to the Sensor end of the track. Print both graphs.
Question 4. Explain how each graph indicates positive and negative velocities.
Select the portion of your x vs. t graph that has a positive
slope by clicking and dragging the cursor to form a rectangle
enclosing this section as shown on the right. Click on the Fit
button above the graph and select Linear Fit. In your
notebook record the equation of the curve as a physics
equation. The computer will give you the slope and yintercept of the generic equation:
x
y = mx + b
t
b is the vertical intercept
m is the slope
The equation of physics is
x = xo + vt
i.e., b = xo, units of meters, and m = v, units of m/s.
Question 5. What is the equation of physics that describes the motion of your cart? You should
write the above equation with values of xo and v (with units) taken from the computer curve fit
analysis. How does the value of v derived from the x vs. t graph compare to the value you read
off directly from the v vs. t graph?
Question 6. How do the graphs you generated in class today connect to the graph you designed
prior to lab? Are there still some ideas that you need to clarify? Can you connect each important
term to a graph or activity that you did? Create a chart that shows the important terms and where
they were experienced in the lab activity.
Question 7: Apply these concepts to real –life examples. Why is it important to study these
concepts?