Physics Simulation
Velocity vs. Stopping Distance
[Lab Index]
BHS
-> Staff
-> Mr. Stanbrough ->
AP Physics -> Kinematics
-> this page
The
Problem:
How is the velocity of a car related to the
distance it takes the car to stop?
The answer is both important and counterintuitive. This simulation
and its companion
experiment should enable you to determine this relationship. This
simulation should familiarize you with the theory and show you how to
do the data analysis. The experiment will let you confirm that the
"real world" actually does work that way. You will operate this
simulation as a "virtual experiment" - collecting data on starting
velocity vs. stopping distance for a range of starting velocities,
then analyzing this data.
The Theory:
Since we are considering the acceleration of the car constant, the
kinematics equation:
should apply. The final velocity, v, of the car is zero, so
solving for x gives:
Which implies that the stopping distance is proportional to the
square of the starting velocity - double the starting speed
means 4 times the stopping distance!
The Simulation:
- Open the Interactive PhysicsTM program.
- Set the simulation
accuracy to "Accurate".
- Create a
rectangle object ()
to represent the car.
- Open the
Properties Window for the "car" and set
- x = 0.0 m
- y = 0.0 m
- Create a position
meter ("x graph") to record the position of the "car". Use the
pulldown menu in the upper-left corner of the meter to a digital
display.
- Create a second rectangle object to represent the road. Use
the mouse to stretch the "road" horizontally. You might want to
zoom out ()
to get a reasonable length for the road, and use the scroll bars
to position everything conveniently.
- Anchor ()
the "road" so it doesn't fall when you start the simulation.
Running the Simulation:
- Set the
car's velocity to 10 m/s (vx = 10.0 m/s) and
run the simulation. The
"car" should gradually come to a stop. Adjust the car's starting
velocity to get the maximum velocity that doesn't let the car fall
off the end of the road. (!!)
- You need a data table. I suggest that you open
the Graphical AnalysisTM program and type
your data directly into its data table - no paper and pencil
needed! (Remember to relabel
the data from "X" and "Y".)
- For each trial, set the car's starting velocity, then run the
simulation. You can read the car's stopping distance from the
position meter. Record your data. Try as wide a range of
velocities as possible - and don't worry, you won't collect too
much data.
Results:
- Construct a graph of starting
velocity vs. stopping distance. Since velocity is the quantity
that you changed (the independent variable), it, by convention,
goes on the horizontal axis.
- Find the best
smooth curve that fits your data.
- Theory predicts that stopping distance is proportional to the
square of the starting velocity. Possibly your data fit
from the last step resulted in an exponent for v close to 2 -
possibly not. It can be difficult to judge whether a set of data
points fall along a parabola or some other curve, but it is
relatively easy to tell whether or not a set of data points fall
along a straight line. If it is true that x is proportional to
v2, then a graph of v2 vs. x will be a
straight line. Here's how to check it using the Graphical
AnalysisTM program::
- Add a
new data column to your data table.
- Change the
column heading of this new column to the formula
"=v^2". The units are (m/s)^2.
- Create a new graph, and graph v2 vs. x. For this
graph, try either a linear curve fit or a regression
line and regression
statistics.
Conclusions:
- So, what do you think? Remember that this is a simulation, and
it doesn't really "prove" anything about the "real
world". Probably the best you can do is say that the
simulation agrees with the theory, or it doesn't, and tell why you
think so.
- What was the car's acceleration in this simulation? Figure it
out analytically and show your solution, and then add
an acceleration meter to your simulation to check your result.
(Hint: What is the slope of the v2 vs. x
graph?)
[Lab Index]
BHS
-> Staff
-> Mr. Stanbrough ->
AP Physics -> Kinematics
-> this page
last update July 11, 2000 by JL
Stanbrough