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 53.0 m. After t1 = 5.00 s, 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. 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 minus t1. 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)?

Explanation / Answer

The displacement of the car from t1 is: Dcar = 53 + 18*t m The displacement of the motorcycle from t1 is: Dmc = 18*t + 0.5*a*t^2 = 18*t + 2*t^2 m The motorcycle catches up with the car when Dcar = Dmc so 53 + 18*t = 18*t + 2*t^2 t = t2 - t1 = sqrt(53/2) = 5.148 s Distance travelled by motorcycle = displacement of car from t1 to t2 = 53 + 18*5.148m = 145.664m

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