# The Two Cars Problem

[Lab Index]

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

## The Problem:

A taxi is stopped at a stoplight. Just as the light changes to green, a second car with constant velocity __v__ passes the taxi. If the taxi can accelerate at __a__ m/s2, how much time will elapse before the taxi catches up to the other car, and how far will they have traveled?

## The Simulation:

Here is a method to set up this simulation:

### Preliminaries:

1. Open the Interactive Physics program.
2. It will be really handy to resize the window to make it longer horizontally, but that's up to you.
3. Turn gravity off.
4. Set the accuracy. You want the simulation to be as accurate as possible, so select "Accurate" and change the Animation Step to 0.010 s. .

### Create the Objects:

1.  Here is a sample Properties Window for the "Other Car" A sample Properties Window for the taxi. A sample Properties Window for the force.
Create a 2 new objects - size and shape don't matter.
2. Object 1 will represent the car moving at constant velocity. Open its Properties Window and set:
1. x = 0.0 m
2. vx = the value for "v" given by your instructor.
3. vy = 0.0 m/s
3. Object 2 will represent the taxi. Open its Properties Window and set:
1. y = 0.0 m
2. vx = 0.0 m/s
3. vy = 0.0 m/s
4. mass = 1.0 kg (This is important! It is how we will get the taxi's acceleration set - using Newton's Second Law.)
4. Create a force () whose point of application is the center of mass of the taxi (Object 2). Open its Properties Window and set:
1. Fx = the value of "a" you are using in this problem.
2. Fy = 0.0 N

Notice that the names of the objects have been changed from "Square 1" to "Other Car" and from "Square 2" to "Taxi" in the Properties Window and the meters in this simulation. Although it does not affect the operation of the simulation in any way, it is convenient to give the objects meaninful names, so that you can keep them straight. This is easy to do using the Appearance Window.

1. Add a clock (Time meter) to the simulation.
2. Add a Position meter (X direction) for each car. Digital readout will probably be best.

 Here is what this simulation might look like when it is ready to run. This is the same simulation, but text and graphics have been added to "spice up" the look of the simulation. The pictures do not affect the operation of the simulation in any way, but they can add interest and be fun, and are easy to add.

## Run the Simulation:

If you haven't done so already, zoom out () a little bit in order to see as much of the "race" as possible. Keep in mind, though, that you don't really need to see the cars - you just need to see the meters.