Race car driver accelerates against another souped-up stock car-physics problem?

Question

A race car driver has a car that can accelerate at 5.9 m/s~2 (meters per second squared). He races against a souped-up stock car. Both start from rest, but the stock car leaves 1.0 seconds before sports car. The stock car moves with constant acceleration of 3.6 m/s~2 (meters per second squared).

1) Find time it takes for race car to overtake stock car
2) Find the distance that they go before they are side by side
3) Find velocity of both cars when they are side by side

Answer 1

A lot of problems can be solved algebraically.
Assume it takes t seconds for race car to catch stock car. At that time the stock car drove for t+1 seconds. I think that you know the distance driven is 0.5a*t^2 if any car started from rest.
0.5*5.9*t^2 = 0.5*3.6*(t+1)^2
Expand and rearrange, we have:
2.3t^2 - 7.2t - 3.6 = 0
This is a quadratic equation, the solution is:
t = (7.2 +- sqrt(7.2^2 + 4*2.3*3.6))/(2*2.3)
= 3.57 or t = -0.439
(1) it takes 3.57s for race car to overtake stock car.
(2) the distance that they go before they are side by side is: 0.5*5.9*t^2 = 37.6m
(3) At that time the velocity of the race car is 5.9t = 21.1(m/s), and the velocity of the stock car is 3.6(t+1) = 16.4(m/s).