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 57.0m . After t1 = 3.00s , the motorcycle starts to accelerate at a rate of 8.00m/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

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.

I am having a hard time with this question, could someone please clearly explain how to do both parts of this question

Explanation / Answer

a)

initially relative speed of motorcycle with respect to car =u = 0

s = ut+1/2*at^2

so,

t = sqrt(2*s/a) = sqrt(2*57.0/8) = 3.775 sec

t2-t1 = t = 3.775 sec

b)

distance travelled by motorcycle = d+distance travelled by car in that time = 57.0+20.5*3.775 = 134.3875 m

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