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 20.5m/s , and the distance between them is 60.0m . After t1 = 4.00s , the motorcycle starts to accelerate at a rate of 6.00m/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 t2?t1 .

Here is the answer to the question : 4.47s

I need help with how to solve it for study purposes. Please show your work. =)

Explanation / Answer

so x motorcyle = 20.5 (t2-t1) + 0.5*6*(t2-t1)^2

xcar = 60 + 20.5*(t2-t1)

we want xcar = xmotorcyle

20.5 (t2-t1) + 0.5*6*(t2-t1)^2= 60 + 20.5*(t2-t1)

so 3*(t2-t1)^2 = 60

(t2-t1)^2 = 20

t2-t1 =sqrt(20) = 4.47 s

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