Question

A police car is traveling at a constant velocity 18 m/s north, when a car zooms by at a constant velocity 42 m/s due north. After a reaction time of 0.8 s the police car pursue the speeder with an acceleration of 5 m/s2. How long (in s) does it take for the police car to catch the speeder? Include reaction time of police car.

Answer 1

d1 = V*t = 42m/s * 0.8s = 33.6 m. Head start for the speeder.

d2 = d1 + 33.6 m.

20*t + 0.5*a*t^2 = 42*t + 33.6
20t+ 0.5*5*t^2 = 42t + 33.6
2.5t^2 -22t = 33.6
2.5t^2 - 22t - 33.6 = 0
Use Quadratic Formula.
t = 10.13 s.