Question

A police car is traveling at a velocity of 18.0 m/s due north, when a car zooms by at a constant velocity of 42.0 m/s due north. After a reaction time of 0.800 s the policeman begins to pursue the speeder with an acceleration of 5.00 m/s2. Including the reaction time, how long does it take for the police car to catch up with the speeder?

Answer 1

Answer:

   t = 10.4 s

Explanation:

given,

velocity of the police car = 18 m/s

reaction time of policeman = 0.8 s

acceleration of the policeman to catch up the speeder = 5 m/s²

time taken to catch the speeder be t₁

distance traveled by the police and the speeder will be same

$D_p = D_s$

$u t_1 + \dfrac{1}{2}at_1^2 = u' t_1$

$18\times t_1+ 0.5 \times 5\times t_1^2= 42\times t_1$

$2.5 t_1^2 - 24 t_1 = 0$

$(2.5 t_1 - 24)t_1 = 0$

$t_1 = \dfrac{24}{2.5}$

t₁ = 9.6 s

total time taken by the policeman

     = reaction time + t₁

     = 0.8 + 9.6

     t = 10.4 s

Total time taken by the policeman to catch the speeder is 10.4 s