A motorcycle is following a car that is traveling at constant speed on a straigh

Question

A motorcycle is following a car that is traveling at constant speed on a straight highway. Initially, the car and the motorcycle are both traveling at the same speed of 18.0 m/s, and the distance between them is 58.0 m . After t1 = 5.00 secs, the motorcycle starts to accelerate at a rate of 4.00 m/s^2 . The motorcycle catches up with the car at some time t2 . A) How long does it take from the moment when the motorcycle starts to accelerate until it catches up with the car? In other words, find t2-t1 Express the time numerically in seconds using three significant figures. B) How far does the motorcycle travel from the moment it starts to accelerate (at time t1 ) until it catches up with the car (at time t2)? Should you need to use an answer from a previous part, make sure you use the unrounded value. Answer numerically in meters using three significant figures.

Explanation / Answer

Assume the time taken by the motor cycle to reach the car to be t seconds (actually t=t2-t1) and the distance for the car, 18=x/t so x=18t for the motor cycle, d = ut + a(t^2)/2 a = 4m/s^2 and with initial velocity (u) = 23m/s 58+x = 18t + 4(t^2)/2 58+18t = 18t + 2(t^2) 58 = 2(t^2) t^2 = 58/2 so, t=5.39 x=18t, so, x=96.9 total distance covered by the motor cycle in time t, 58+x = 154.93 m

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