Question

Can you please explain me this question step by step?

Thank you so much

Answer 1

Suppose the trooper takes t sec to catch the speeding car.

So, distance covered by the trooper in t sec -

s1 = u*t + (1/2)*a*t^2

Since, initial speed of the trooper, u = 0

So, s1 = 0 + (1/2)*3.0*t^2 = 1.5*t^2

Now, as per the given condition, the trooper starts her journey 1 sec after the speeding car passes it.

So, distance covered by the car in this time -

s2 = (t+1)*v = (t+1)*45 m

To overtake the car, we should have -

s1 = s2

=> 1.5*t^2 = (t+1)*45 m

=> 1.5t^2 - 45t -45 = 0

=> t = [45 + sqrt(45^2 + 4*1.5*45)] / (2*1.5) = [45 + 47.9] / 3.0 = 31.0 s (Answer)

Other value of t is negative so, it can be discarded.