Physics 125 – Mesa College
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Your Name:
Linear Kinematics
Group Name:
& Constant Acceleration
Lab Day:
Objective: To understand the relationship between displacement, velocity and constant
acceleration; To determine the average acceleration of an object by multiple techniques;
To evaluate the effectiveness of these techniques; To become familiar with various
graphical representations of the movement of an object.
Hypothesis: Any object that moves in a straight line with constant acceleration will display
certain characteristics that can be used to deduce the magnitude of that acceleration. By
graphically representing the data obtained by studying such an object, various physical
quantities can be established.
Mathematical Models and Reference Values Used: Using the definition of velocity as the
ratio of the displacement to the elapsed time allows the creation of vector equations of
motion that describe the behavior of an object with constant acceleration.
 

The displacement as a function of time: x f − xo = Δx = vot + 12 at 2
  
The velocity as a function of time: v f = vo + at
These functions can be represented in table or graph format. We will produce graphs of the
object’s motion on both Cartesian and Logarithmic scales.
In our examination of objects falling near the surface of the earth, it is seen that all
objects have the same acceleration g, which has an accepted value of 9.81 m/s2. Objects
that slide down inclined surfaces will display a lesser acceleration proportional to the angle
of inclination. On a horizontal surface, there should be no acceleration due to gravity.
Equipment List: Air Track, Blower & Hose, Jack, 1 & 2 Meter Sticks, 30 cm Ruler, Glider,
Glider Accessory Kit, 50 g Glider Masses, Ring Stand, Tape Timer, White Paper Tape,
Masking Tape
Setup and Procedure
1. Place the glider in the middle of the track and turn on the blower. If the track is level,
the glider should remain motionless or gently drift back and forth near the middle of the
track. If the glider moves towards one end of the track, level the air track by adjusting the
screws in each leg. If this step is not properly completed the experiment will show large
errors.
2. Place the jack underneath the single leg support to raise the end of the track by about
10 cm.
3. Use the 30 cm ruler to measure the height (H) of the jack and record it in Data Table
One. Also verify that the distance (D) between the leg supports is 100 cm.
4. Turn off the blower and position the glider on the raised end of the track. Adjust the
angle of the tape timer to match the angle of the surface of the track, and adjust the
height of the tape timer to be about 1 cm above the top of the glider.
Revised COM 08/2013
Physics 125 – Mesa College
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Data Table One
D = distance between supports (cm)
H = height of jack (cm)
Q1. The ‘downhill’ acceleration of the glider is proportional to the angle at which the track
is inclined. The larger the angle of inclination of the track, the greater the acceleration of
the glider. In particular, the theoretical acceleration of the glider is given by (|g|H/D). Use
your values to calculate atheory. Show your work with units then record the result in Data
Table Three.
5. Unroll a piece of white paper tape that is slightly longer than the glider track and detach
it from the rest of the roll. Thread the tape through the slots on the top of the tape timer
and between the metal bar and the carbon paper disc. Use masking tape to attach one end
of the paper tape to the top of the glider.
6. Place two 50-gram masses on each side of the glider. Prevent the glider from moving
then turn on the blower. Allow the air to circulate for at least 30 seconds. Set the switch
on the tape timer to the 10 Hz setting. The tape timer will make 10 marks on the paper
each second, so the time between successive dots is 0.1 seconds.
7. Have a group member prepare to catch the glider at the bottom of the track, then
release the glider. Turn off the tape timer and inspect the white paper tape for missing or
double dotted points. Repeat the data run if necessary. Once you have a satisfactory data
run notify your instructor. Your instructor will choose an arbitrary point that you will
treat as your first data point.
8. Attach the paper tape to a two-meter stick to make measurements simpler. From the
first point chosen by the instructor, measure each position of the glider and record the
results in column 1 of Data Table Two.
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Physics 125 – Mesa College
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Q2. Show one sample calculation of Δx and vavg during a 0.1 second interval. Show all work
with units, then complete columns 3) and 4) in the data table in the same way.
Data Table Two
Dot
1) x (cm)
2) t (s)
1
0
0
2
0.1
3
0.2
4
0.3
5
0.4
6
0.5
7
0.6
8
0.7
9
0.8
10
0.9
11
1.0
12
1.1
13
1.2
14
1.3
15
1.4
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3) Δx (cm)
4) vavg (cm/s)
5) xc (cm)
6) tc (s)
Physics 125 – Mesa College
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Q3. Use one value from the beginning and one from the end of your data set to calculate
the acceleration of the glider. The acceleration depends on the instantaneous velocity of
the glider, but your data only indicates the average velocities of the glider. However, the
mean-value theorem offers a solution. For constant slope intervals, the average value of
the function over the entire interval is the same as the value of the function at the
midpoint of the interval. So, the average value is the same as the instantaneous when
 
v f − vo

t=0.05 s, 0.15 s, 0.25 s, etc. Use atable =
to calculate the glider acceleration. Show
t f − to
your work with units and transfer your result to Data Table Three.
Graphical Analysis
Please make sure you have read and understood the “How to Draw a Graph” download from
the course website before proceeding.
Position as a function of time
Q4. Using a Cartesian coordinate system, construct a graph of the position of the glider as a
function of time. Draw the smoothest curve possible. Then draw a line tangent to the graph
at t=0.4 seconds and a second tangent line at t=1.0 seconds. Make sure the lines are long
enough to accurately determine the slope of each tangent line. The slope of the line
tangent to the position graph is the same as the value of the instantaneous velocity of the
glider. Calculate the slope of each tangent line units and record the results here.
v5 =
v11 =


v −v

Use axvt = 11 5 to calculate the glider acceleration. Show your work with units and
1.0s − 0.4s
transfer your result to Data Table Three.
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Physics 125 – Mesa College
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Instantaneous velocity as a function of time
Please make sure to place the y-axis about one-third of the way from the left edge of the
paper in order to leave enough room to find the time intercept.
Q5. Using a Cartesian coordinate system, construct a graph of the instantaneous velocity of
the glider as a function of time. Remember that the instantaneous velocities occur at the
midpoint of the time intervals so you will be using time values of 0.05 s, 0.15 s, 0.25 s, etc.
Once you have constructed the graph, draw a best-fit line to your data and extend the line
all the way to the time axis. Note: The point where your line crosses the velocity axis when
t=0. This intercept represents the velocity of the glider at the arbitrary start time chosen
by your instructor. Call this value vo and record it here with proper units:
vo =
Q7. Use your best-fit line from the graph and calculate the glider acceleration using
 
v f − vo

. Show your work with units and transfer the result to Data Table Three.
avvt =
t f − to
Q6. Evaluate the equation for the position of the glider as a function of time when t = 1.0
seconds. Use xo = 0, but use vo obtained in Q6 to represent the initial velocity of the glider.
1


Using x f = 0 + vot + avvt t 2 , substitute your values and show your work with units to predict
2
the position of the glider when t = 1.0 seconds.
xf =
Compare this result to the value recorded in your data table for t = 1.0 seconds and
calculate the percent difference between the two quantities. Show your work with units.
% Difference =
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Physics 125 – Mesa College
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Data Table Three
Source
Value (units)
Theoretical Calculation (atheory)
Data Table (atable)
Position v Time Graph (axvt)
Velocity v Time Graph (avvt)
Q7. Compare the following accelerations, calculating either ‘Percent Difference’ or
‘Percent Error’ as appropriate. Show all work with units.
[table v position(xvt)]
=
%
[theory v position]
=
%
[theory v velocity]
=
%
[table v velocity(vvt)]
=
%
[theory v table]
=
%
[position v velocity]
=
Revised COM 08/2013
%