Question #3997

Two cars travel simultaneously at a common point. Car A travels at a rate of 25 m/s and accelerates at 2.5 m/s2 . Car B starts from rest and accelerates at 7.5 m/s2. How long will the two car cover the same displacement?

Expert's answer

Let's construct the system of two equations of motion, for the car A and B respectively:

x = x_{0} + v_{0}t + a_{1}t^{2}/2

x = x_{0} + a_{2}t^{2}/2

0 + 25t + 2.5 t^{2}/2 = 0 + 7.5t^{2}/2

25t = 5t^{2}/2

t = 10 sec

x = x

x = x

0 + 25t + 2.5 t

25t = 5t

t = 10 sec

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