A motorcycle waits at a stoplight next to a Porsche. When the light turns green

Question

A motorcycle waits at a stoplight next to a Porsche. When the light turns green at t = 0 seconds, both vehicles proceed toward the next intersection, 250 feet away. The motorcycle crosses the intersection at t = 5 with instantaneous velocity 60 ft/s. The Porsche crosses the intersection at the same time, with instantaneous velocity 70 ft/s. (a) What is the average velocity of the motorcycle between t = 0 and t = 5? What is the average velocity of the Porsche over the same time interval? (b) If f?(t) is the instantaneous velocity of the motorcycle, what is the area under the graph of f?(t) from t = 0 to t = 5? (c) Explain why the instantaneous velocity of the motorcycle must have exceeded that of the Porsche at some time in the interval [0, 5].

Explanation / Answer

a)average speed = 250/5 =50ft/s

avg speed is same for both bike and porsche since avg speed = total distance travelled/ total time taken

b)250ft ( since whatever the speed is total distance covered = 250 ft)

c)as both travel 250 ft in 5 secs ,and at the end as Vporsche>Vbike, Vbike should have exceeded Vporsche sometime in between to compensate the distance

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