Pictorial Models

When first solving a problem, our initial concern should not be with specific numbers and calculations, but with simply understanding the information in a useful way.

The Pictorial Model is a good way to do this.

A Pictorial Model should include:

• A sketch of the situation, showing each object
  • at the beginning of the motion,
  • the end of the motion,
  • and at any point in between where the character of the motion changes.
• A coordinate system that you impose on the problem, including a choice of the origin, the axes, and the positive direction.
• Symbols, on the sketch, to show position, velocity, and time with subscripts for each time an object is shown on your sketch. Also, show symbols for other relevant quantities such as mass.
• An arrow indicating the direction of the acceleration vector or vectors. Write a = 0 if the acceleration is zero.
• A table listing the values for all quantities given in the problem, or that can be found quickly using geometry.
• A list of the unknown quantities you have been asked to find.

Example 1-7:

(1) Draw a pictorial model for the following problem: Billy jumps on his bike pedals away with a constant acceleration. How far has he traveled after 5 seconds, when his speed is 6 m/s?

(2) Draw a pictorial model for the following problem: Martha is riding her motorbike on a closed airstrip course at 120 mph when she passes a cone by the side of the airstrip. After 0.5 s, she applies the brakes, and brings her motorbike to a stop in 2.5 s, with a constant deceleration. How far from the cone does she come to a stop?