Superguy has attached a nitro booster to his motorcycle to assist him in his que

Question

Superguy has attached a nitro booster to his motorcycle to assist him in his quest to rid Science City of his archenemy, Mad Maxwell. The motorcycle doubles its acceleration when the nitro is activated. Superguy is idling by the side of the highway when Maxwell tears by. At this instant Superguy steps on the gas and accelerates at a constant rate until he is moving at the same speed as Maxwell, then uses his booster to close the distance and catch Maxwell. Maxwell moves at a constant 30.0 m/s the entire time, and is caught 60.0 seconds after passing Superguy. (a) How far does Maxwell travel after passing Superguy before being caught? (b) What is the acceleration of the motorcycle with the nitro booster engaged? (c) How long is Superguy in motion before engaging the booster?

Explanation / Answer

a) Maxwell races at 30.0 m/s when he passes Superguy. That is at x = 0. After 60 seconds he is 30.0 * 60 m away = 1800 m.

b) When superguy starts he is at x = 0 and v =0 and a certain acceleration a.
He accelerates until he is at the same speed as Maxwell, so until v = 30.0 m/s
Use v = a. t so at t1 = 30.0/a he has attained the same speed.
The road he traveled is (1/2).a.t12 = 450 / a.
Then he turns on the booster and accelerates with 2 times a, that is 2.a
He catches up with Maxwell after t2 seconds since starting the booster.
The road traveled with the booster on is (1/2).2a.t22
But t2 + t1 = 60 and t1 = 30.0 /a
Thus  solving we get a = 1.17m/s2

Acceleration with nitro booster engaged = 2 X1.17 = 2.34m/s

Time before engaging the booster = 30/1.17 = 25.6 s

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