A car is speeding at 33.4 m/s. A police car starts in pursuit from rest when the car is 100 m past the cruiser. At what rate must the cruiser accelerate to catch the speeder before the state line, 1.2 km away from the speeding car?

Question

A car is speeding at 33.4 m/s.  A police car starts in pursuit from rest when the car is 100 m past the cruiser.  At what rate must the cruiser accelerate to catch the speeder before the state line, 1.2 km away from the speeding car?

Include all steps if possible please, so that I may fully understand.

Henry · Answer

d = r*t = 1200 m.
33.4t = 1200,
t = 1200 / 33.4 = 35.93 s. = Time to reach state line.

Dt = 100 + 1200 = 1300 m. = Dist. the
trooper must travel to reach state line.

Dt = 0.5a*t^2 = 1300 m.
0.5a*(35.93)^2 = 1300,
0.5a*1291 = 1300,
645.5a = 1300,
a = 1300 / 645.5 = 2.014 m/s^2.