Kinematics problem(already have the answer, but i need an someone to explain it to me

[ihatecats2014]

Homework Statement

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 48.0mph , and the distance between them is 60.0m . After t1 = 5.00s , the motorcycle starts to accelerate at a rate of 7.00m/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?

the answer is 4.14s

i always seem to have problems with questions that are framed in this way. can someone walk me through the steps? help would be greatly appreciated

oh and these are the equations
x=volt+1/2at^2
t2-t1

 

[ponjavic]

You can ignore the first part up until t1 = 5s as the distance between the two objects remain 60m.

What happens then is x1 - x2 = 0 where x1 = s1_0 + v1_0*t and x2 = s2_0 + v2_0*t + 1/2*a2*t^2.
(x_1 is not experiencing any acceleration so a1 would be 0)

We also know that s1_0-s2_0 = 60. Also v1_0 = v2_0. After rearranging:
s1_0 - s2_0 + v1_0*t - v2_0*t - 1/2*a2*t^2 = 0
1/2*a2*t^2 = 60.