Answer:
8.13 seconds
Step-by-step explanation:
Given that a police car is traveling at a velocity of 17.0 m/s due north, when a car zooms by at a constant velocity of 40.0 m/s due north. After a reaction time 0.300 s the policeman begins to pursue the speeder with an acceleration of 4.00 m/s^2. Including the reaction time, how long does it take for the police car to catch up with the speeder
First calculate the acceleration of the speeder
V = U - at
0 = 40 - a × 0.3
0.3a = 40
a = 40/0.3
a = 133.3 m/s^2
The speeder distance covered will be
V^2 = U^2 - 2as
0 = 40^2 - 2 × 133.3 × S
266.67S = 1600
S = 1600/266.7
S = 6 m
Let's calculate the time to reach the distance by using second equation of motion
S = Ut - 1/2at^2
6 = 17t - 0.5 × 4 t^2
6 = 17t - 2t^2
2t^2 - 17t + 6 = 0
t^2 - 17/2t = - 3
(t - 17/4)^2 = 18.06 - 3
(t - 17/4)^2 = 15.06
t - 17/4 = 3.88
t = 17/4 + 3.88
t = 8.13 seconds
Therefore, it take 8.13 seconds for the police car to catch up with the speeder