Question

A car traveling at a constant speed of 45.0 m/s passes a trooper hidden behind a billboard. One second after the speeding car passes the billboard; the trooper sets out from the billboard to catch it, accelerating at a constant rate of 3.00 m/s 2 . How long does it take her to overtake the car?

Answer 1

Let it catch the car at Distance = S

Let Say time taken to over take = t sec

So other car traveled for   =  t+1 sec

S = ut + (1/2)at²

for first car u = 45 m/s   , a = 0 as constant speed , t = t+1

S = 45(t+1)

for second car u = 0  a = 3m/s² t = t

S = (1/2)3*t²

45(t+1) = (1/2)3t²

90(t+1) = 3t²

30(t+1) = t²

t²-30t-30 = 0

solving this we get

t = 15+√255 = 30.97 sec

t = 15-√255 is -ve and can not be a solution

so 30.97 s is answer

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