Answer:
11.1 s
Explanation:
Speed of the police car as given = v = 18 m/s
Speed of the car = V = 42 m/s
Reaction time = t = 0.8 s
Distance traveled by the police car during the reaction time = d₁= 0.8 x 18 = 14.4 m
Distance traveled by speeding car = d₂ =0.8 x 42 = 33.6 m
Acceleration of the police car = a = 5 m/s/s
The police car can catch the speeding car only if it travels a distance equal to the speeding car in a time t.
Distance traveled by the police car = D = d₁ + v t +0.5 at², according to the kinematic equation.
⇒ D = 14.4 + 18 t + 0.5 (5) t²
⇒ D = 14.4 + 18 t+2.5 t² → (1)
For the speeding car, distance traveled is D = 33.6 + 42 t, since it is constant velocity. Substitute for D from the above equation (1).
⇒ 14.4 + 18 t+2.5 t²= 33.6 + 42 t
⇒ 2.5 t² -24 t - 19.2 = 0
⇒ t = 10.3 s
Total time = t +0.8 s
⇒ Time taken for the police car to reach the speeding car = 10.3+0.8= 11.1 s
