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A speeder passes a parked police car with a speed of 65 km/h in a 50km/h...

A speeder passes a parked police car with a speed of 65 km/h in a 50km/h zone. One second after the speeder has passed the police car, the police begin his pursuit. The police car accelerates with constant acceleration of 2m/s2
(i) How long does it take for the police to catch the speeding car?

(ii) How far did the police car travel before police caught up with the speeder? (iii) What is the speed of the police car when catches up with the speeder?

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Answer #1

The speed of the police car was initially u = 0 m/s

the speed of the speeder was 65 km / h or 18.06 m/s

let the chase time be t sec

in 1 s the distance between the speeder and police was s = 18.06 (t+1)

The accleration is a = 2 m/s2

i) using the relation

putting the value we get

we get time t =19 s

ii) The distance traveled by the police car is s  

putting the value we get s = 361.2 m

The speed of the police car is

putting the value we get

velocity v = 38 m/s or 136.8 km/h

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