A Person is speeding in a car along a straight part of the freeway with velocity

Question

A Person is speeding in a car along a straight part of the freeway with velocity v_0 A Police car sitting on the side of the road takes off following the speeding car. The police car accelerates with constant acceleration, a_1, until reaching velocity v_1 (v_1 > v_0). Police keeps constant velocity v_1 until catching the speeding car. Find how long time it takes for the Police car to reach the speeding car (which keeps on driving with constant.v_0. Find the time if v_0 = 150 km/h v_1 = 180 km/h a_1 = 2 m/s^2

Explanation / Answer

person car velocity , V0 = 150 km/h = 150*1000 / 3600 = 41.67 m/s

police car velocity, V1 = 180 km/h = 180*1000 / 3600 = 50 m/s

police car acceleration,a1 = 2m/s2

distance travel by person car,d0 = V0*t [ velocity = distance / time]

d0 = 41.67*t

distance travel by police car =d1

from S = u*t + (1/2)*a*t2

here S = d1, u = initial velocity of police car = 0 ( due to at rest initially)

d1 = 0*t + ( 1/2)* 2*t2

d1 = t2

police car will reach to the speeding car if they travel equal distance in equal time t.

that is , d0 = d1

41.67*t = t2

t = 41.67 s   

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