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 22.5 m/s , and the distance between them is 52.0 m . After t1 = 3.00 s , the motorcycle starts to accelerate at a rate of 4.00 m/s2 . 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 t2t1 .

Express the time numerically in seconds using three significant figures.

Explanation / Answer

using the equation of motion

s = ut+ 0.5*at^2

{ s is displacement,u is initial velocity of motocycle, a is acceleration and t is time taken to cover s distance }

52 = 22.5*t + 0.5*4*t^2

t = 1.967 sec

time taken to catch the car after acceleration of 4m/s^2 is 1.967 seconds

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