Question

Two rather unequal cars are competing in a drag race. For simplicity, let's assume that the accelerations of the cars are constant. Car 1 has an acceleration of 3.3 m/s2, while Car 2 has an acceleration of 5.9 m/s2. Car 2 gets off to a late start, 0.5 seconds after Car 1.
1. At what time after Car 1 took off will it be overtaken by Car 2?
2. How far down the track will this happen?
3. How much faster will Car 2 be than Car 1 by that time?

Answer 1

Answer:

car1: a=3.1m/s^2 , car2: a=6.1m/s^2

(a) 1/2*3.1*t^2= 1/2*6.1*(t-0.9)^2

1.55t^2= 3.05(t^2-1.8t+0.81)= 3.05t^2-5.49t+2.4705

1.5t^2-5.49t+2.4705= 0

t= 3.13457 = 3.14[s] after.

(b) d= 1/2*3.1*3.13457^2= 15.23[m] approx.

(c) car1: v=at = 3.1*3.13457= 9.717m/s

car2: v=at = 6.1*(3.13457-0.9)= 13.631m/s

13.631-9.717= 3.914 = 3.91[m/s] faster than car1.