Question

A car speeds past a policeman motorcycle at a constant speed. After 2 sec, the policeman begins to chase the car at an acceleration of 6.5 m/ s^2 until he reaches 110 km/hr. He reaches the car at 1.4 km. What speed was the car speeding at?

Answer 1

here,

let the time taken by the police car be t and the initial speed be u

u * (t + 2 ) = 1400

t = 1400/u - 2 ..(1)

for the police man

final speed of police man , v = 110 km/h = 30.6 m/s

time taken to attain maximum speed be t'

v = 0 + a * t'

30.6 = 6.5 * t'

t' = 4.7 s

the distance travelled by police man , d = 1.4 km = 1400 m

v^2 /(2a) + v * ( t - t') = 1400

30.6^2 /( 2 * 6.5) + 30.6 * ( (1400/u - 2 ) - 4.7) = 1400

solving for u

u = 27.9 m/s

the constant speed of car is 27.9 m/s