M. Paetkau Physics/Math
Instantaneous Speed vs Ave Speed
Fred the flying police officer patrols highway 97 between Penticton and Summerland for the Penticton RCMP. He is responsible for catching speeders along a stretch of road where the speed limit is 100km/h. Due to cutbacks he is not equipped with Doppler laser or other fancy radar equipment, but only a stopwatch. He also knows the distance between two obvious landmarks on the road.
How can he identify speed violators?
On a particular day, Silvie, from the RCMP detachment in Summerland has set up a speed trap of her own using a radar gun. She is placed just after a corner in the highway where she can get a reading of the cars as they come around the corner before they spot her. Her location is between the two landmarks used by Fred. If she detects a speeder, two police further down the road pull the car over and issue a ticket
Now on this particular day, Fred is tracking a red BMW heading north as a possible speeder. The Beemer is alerted by drivers heading south of Sylvie’s impending speed trap and slows down in time to not get caught by Sylvie and her team. However, 10 days later a ticket arrives in the mail to the driver of the Beemer. The driver is very upset because clearly he was not speeding through Sylvie’s speed trap, and so takes his case to court where both Fred and Sylvie are to testify. The driver of the Beemer is using Sylvie’s testimony to defend himself of the ticket issued by Fred.
How would the driver use Sylvie in support of his innocence?
Has the driver been wrongly accused by Fred? Work in your group to provide Fred’s defense of the issuance. One group will be called upon to present Fred’s case. Consider a graphical argument, a numeric argument or an algebraic argument.
Another Speed Trap
A car traveling at a speed of 86.4 km/h in a 60 zone passes Sylvie hidden behind a billboard on her motorbike. Sylvie checks for traffic, starts her bike and then sets off in chase with constant acceleration of 3.00m/s2.
How long does it take Sylvie to overtake the speeding car?
How fast is she going at the time?
What have we neglected in this problem and would they contribute to increasing or decreasing the time of interception.
As a general rule, if it will take more than one minute for the police to catch up, Sylvie is required to radio in her pursuit and request backup for interception.
What reasons can you think of for this rule?
If all else were the same, how fast would the car have to be going for it to take a minute for Sylvie to catch up? How fast is Sylvie going after 1 minute?