PHYS 250 Velocity Lab PreLab Assignment
Name _________________________________
Section __________
For each of the two position versus time graphs shown below, sketch (before coming
to lab) the corresponding velocity versus time graphs:
x
(A)
x
(B)
t
t
vx
vx
t
Explain in words how you determined the velocity-versus time graph from the position
versus time graph.
t
PHYS 250 Laboratory #1:
1D Kinematics
Score: _____
Section #:______
Name:_____________________________
Name:_____________________________
Name: _____________________________
Lab-Specific Goals:




To investigate velocity as the time rate of change of position.
To learn to use photogates to determine velocity of an object.
To explore position, velocity, and acceleration graphs.
To develop general graphing skills.
Equipment List:


Airtrack system with one glider
Photogate timer with Accessory Photogate
Introduction and Pre-Lab Questions:
Position of an object is simply the object’s coordinates within a reference frame. For
example, in the coordinate system of latitude and longitude, Penn State is at 40 degrees
48 minutes 07 seconds North latitude and 77 degrees 51 minutes 23 seconds west
longitude. Any coordinate system is arbitrary, but a common coordinate system is
important to communicate information about positions.
Velocity is the time rate of change of position. We learned in lecture that this means that
velocity is the slope of the position versus time graph. If the slope of the position versus
time graph is constant, the velocity of the object is constant; if the slope of the position
versus time graph changes over time, then the velocity of the object changes over time.
Velocity (for one-dimensional motion) can be described as positive or negative
depending on whether the object is moving in the positive direction of the coordinate
system (e.g., to the right for horizontal motion as we have generally made our coordinate
system in class). The sign (+/-) tells us in what direction an object is moving. Velocity
conveys both speed (how fast) and directional information.
Acceleration, which we will be looking at in Activity 2, is the time rate of change of
velocity (just as velocity is the time rate of change of position). So just as velocity (vx) is
the slope of the position (x) versus time graph, acceleration (ax) is the slope of the
velocity versus time graph. And just as displacement is the area under the velocity versus
time graph, so change in velocity is the area under the acceleration versus time graph.
The velocity versus time graph is a valuable tool in analyzing motion since from it we
can get the displacement (area under the velocity versus time graph) and the acceleration
(slope of the velocity versus time graph).
vx = slope of x
x
ax = slope of vx
vx
x = area under vx
ax
vx = area under ax
Activity 1: Measuring Glider Velocity
Set up the air track as shown in the figure below (though we want it level, so we won’t be
elevating one end as shown in the figure).
The photogates will let us find the speed of the glider at different places along the track.
The photogates work in two modes: GATE and PULSE. You will need to know how to
use each mode and when it’s best to use which mode for several labs in this course.
GATE Mode:
Turn on the photogate timer and set it to GATE mode. In this mode, the timer measures
the time interval t that the photogate is blocked by the glider as the glider passes
through the gate. The glider has an effective length L.
Make sure that the glider is gliding freely and smoothly (minimum wobble) as it passes
through the photogates.
The average speed of the glider as the gate passes through the gate is given by
vgate = L/t,
Where t is the time interval recorded by the photogate.
Using 1 photogate in GATE mode:
1. Measure the length L of the flag on the glider.
2. Turn the memory switch to “Off”.
3. Press RESET between readings to zero the timer.
4. Send the glider through the photogate
5. Read off t from the display
Activity 1.1: Set up just one photogate along the track. Before giving the glider a light
push to send it through the gate, carefully make sure that the glider will not collide with
the photogate and that the glider flag is triggering the photogate (i.e., the red LED on the
photogate lights up). Now send your glider through SLOWLY and make sure to catch it
before it hits the opposite end of the track.
L = _____________
t = _____________
Now calculate: speed = __________________
Don’t forget to include units in all the values you report above!
Now send the glider through the photogate faster than before (but be careful not to have it
move too fast!).
L = _____________
t = _____________
Now calculate: speed = __________________
What happened to t when you sent it through faster? ____________________________
What happened to v=L/t when you sent it through faster? ________________________
You can use a second photogate in GATE mode to get a second measurement of speed.
Using 2 photogates in GATE mode:
1. Measure the length L of the flag on the glider.
2. Flip the memory switch to “On”.
3. Send the glider through both photogates.
4. The time displayed on the screen is the time that the first photogate triggered was
blocked. (We’ll call that t1.)
5. Toggle the memory switch to “Read” and another time will be displayed. This
time is the total time that the photogates were blocked, or t1 + t2, where t2 is
the time the second photogate triggered was blocked.
Activity 1.2: Add the second photogate to the track. Once again, carefully make sure that
the glider will not collide with the added photogate and that the glider flag is triggering
the photogate (i.e., the red LED on the photogate lights up). Now send your glider
through and make sure to catch it before it hits the opposite end of the track.
L = _____________
t1 = _____________
t1 + t2 = _____________
t2 = _____________
Speed through first photogate = __________________
Speed through second photogate = __________________
Don’t forget to include units in all the values you report above!
PULSE Mode:
Turn on the photogate timer and set it to PULSE mode. You will need to have two
photogates on the track, separated by a distance D. In PULSE mode, the timer measures
the time interval t between when the first photogate is blocked by the glider and when
the second photogate is blocked.
The average speed of the glider as it moves between the two gates is given by
vpulse = D/t,
Where t is the time interval recorded by the photogates.
Using PULSE mode (two photogates):
1. Measure and record D, the distance the glider moves on the air track from
where it triggers the first photogate, to where it triggers the second photogate.
(Move the glider and watch the LED on top of the photogate. When the LED
lights up, the photogate has been triggered.)
2. Turn the memory switch to “Off”.
3. Press RESET between readings to zero the timer.
4. Send the glider through both of the photogates
5. Read off t from the display
Activity 1.3: Set up two photogates on the track and carefully measure the distance D
between them. Before giving the glider a light push to send it through the gates, carefully
make sure that the glider will not collide with the photogates and that the glider flag is
triggering the photogates (i.e., the red LED on each photogate lights up). Now send your
glider through and make sure to catch it before it hits the opposite end of the track.
D = _____________
t = _____________
Now calculate: speed = __________________
Don’t forget to include units in all the values you report above!
Activity 2: Velocity Graph Exercise
The table below shows the velocity at various times for a runner traveling in a straight
line (which we will call the x-axis).
Time (s)
0
10
15
20
25
30
Velocity (vx) (m/s)
3
4
4.5
5
5.5
6
1) Make a velocity-time graph for the runner on the graph paper provided below. Be sure
to follow rules for making good graphs: make the time and velocity axes linear, use the
space (i.e., don’t make it too small), label the axes, be neat.
2) Show on your velocity-time graph how to calculate the slope between t = 10 and t = 20
seconds.
3) Make an acceleration-time graph for the runner on the graph paper provided below.
Once again, be sure to follow rules for making good graphs.
4) For the interval between 10 and 20 seconds, show on your graphs that the area under
the acceleration-time graph corresponds to the change in velocity during that interval.
5) Make a position-time graph for the runner on the graph paper provided below,
indicating her position at the times provided in the table above. Assume that she starts at
x = 0. [Question to ponder: why can’t you connect these points with straight lines?]
Velocity-Time Graph for Runner
Acceleration-Time Graph for Runner
Position-Time Graph for Runner