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Question

A thief with a stolen car passes through a police check post at his top speed of 90 km per hour a motorcycle cop reacting after 2 seconds accelerates from rest at 5 metre per second square is top speed being 108 km per hour find the maximum separation between police man and thief


Solution

 

After 2s the thief would be at a distance of 50m fromthe police car.We shall consider this to be t=0.

let after a time t the distance be max.

then the distance between the check post and the thief would be 50+25t.......(i)

the police car would be at a distance of 2.5t^2from the check post...........(ii)

 then the distance between them would be x=50+25t-2.5t^2

this would be max when dx/dt=0

which implies dx/dt=25-5t=0

therefore t=5s.hence x=50+125-62.5=112.5(ans)

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