PHYSICS 115’06 CYCLE 1
GROUP SUMMARY PROBLEM: 1D CONSTANT v
I. Skills Practice
1. How many data points (minimum) do you need to find a best-fit linear function to your data?
2. Graph the following motions of a bicycle and a horse using the same axes:
· the bicycle starts first and moves at a steady speed of 2 m/s in the positive x direction.
· the horse starts 2 s after the bicycle and gallops in the same direction at a steady speed of 4 m/s.
· What physical information can be found using the point of intersection of these two graphs?
II. Problem Solving
A state trooper in a police car is traveling along the highway at 50 miles per hour (1 mile = 1.61 km). A speeding car traveling at 80 mph overtakes the police car and continues to move ahead at the same speed. The trooper delays 5 seconds to call in the report on the speeding car to the police station. He then immediately accelerates to 100 mph and pursues the speeder.
Graphical Model :
a) Assume that at t = 0 seconds, the speeding car passes the police car. Draw a position vs. time graph for the speeding car. On the same graph, draw a position vs. time graph for the state trooper. Make the (unreasonable) assumption that the trooper changes velocities instantaneously. Use the graph paper on the next page.
b) Based on your graph, at what time, t, does the trooper to catch up with the speeding car? How far do these cars travel in this time interval?
Analytical Model :
Using the appropriate analytical methods (mathematical statements), determine:
a) how long it takes the trooper to catch up with the speeding car and
b) how far both cars travel in this time.
c) Compare these values with Graphical Model (b) above. If they do not agree, decide which model(s) need revision, and then apply the model(s) again.
Continue your revisions until you are satisfied that both models predict consistent results for both time and distance.