Name  __________________________________ Date ______________  Per _______

How to Make a Motion Map

Modeling Physics

  The modeling method is contains four things:  the Picture, the motion map, graph and mathematical equation.

What is a motion map?

     A motion map shows the position, velocity and acceleration of an object at a certain time.

Cars Traveling at A Constant Velocity

Draw A Picture

If you could take a bunch of pictures to see a car moving to the right at constant velocity where each image showed the position of the car at one-second intervals.

                 1 sec.                       2 sec.                           3 sec.                      4 sec.

Notice:  The car is equal distance from the car in front of it.  The car is traveling at a constant velocity.

Motion Maps

This is the motion map that represents the car. We  show the position of the object with a small point. At each position, the object’s velocity is represented by a vector (the arrow).

                 1 sec.                       2 sec.                           3 sec.                      4 sec.

Notice:  The vectors (arrows) are pointed in the same direction as the car.  They are also the same distance as the vector in front of them.

Car Traveling at Greater velocity

Draw A Picture

If you could take a bunch of pictures to see a car moving to the right at an greater velocity where the images showed the car at one second intervals.

                 1 sec.                       2 sec.                           3 sec.                      4 sec.

Motion Maps

This is the motion map that represents the car.  We show the position of the object with a small point.  At each position, the object’s velocity is represented by the vector.

Car Traveling to the left at a Constant Velocity (picture and motion Map)

If the car were moving to the left at constant velocity, the photo and motion map might look like this:

More complicated motion can be represented as well.

Here, an object moves to the right at constant velocity, stops and remains in place for two seconds, then moves to the left at a slower constant velocity.

Consider the interpretation of the motion map below. At time t = 0, cyclist A starts moving to the right at constant velocity, at some position to the right of the origin.

Cyclist B starts at the origin and travels to the right at a constant, though greater velocity.  At t = 3 s, B overtakes A (i.e., both have the same position, but B is moving faster).

The Graphical Representation

You could also represent the behavior algebraically as follows:

X = v_At + x₀, , for A

X = v_Bt  for B                           where V_B  > V_A