[Lab Index]

BHS -> Staff -> Mr. Stanbrough -> AP Physics -> Kinematics -> this page

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 Physics*^{TM}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 (v
_{x}= 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 Analysis*^{TM}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 v^{2}, then a graph of v^{2}vs. x will be a straight line. Here's how to check it using the*Graphical Analysis*^{TM}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 v
^{2}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 v^{2}vs. x graph?)

[Lab Index] BHS -> Staff -> Mr. Stanbrough -> AP Physics -> Kinematics -> this page

last update July 11, 2000 by JL Stanbrough