car catching car?

Question

A certain automobile can decelerate at |a1| = 1.8 m/s2. Traveling at a constant v1 = 31 m/s, this car comes up behind a car traveling at a constant v2 = 10 m/s.

1) How close to the slower car can the driver of the faster car come before applying his brakes and still avoid a collision?

2) Unfortunately, the driver of the faster car does not apply his brakes until he is just 30 m behind the slower car! Call the instant at which he applies the brakes t = 0.
-------At what time does the inevitable collision of the two cars occur?

3) How far beyond its position at t = 0 does the slower car get before it is hit?

Answer 1

1)
s = (31^2 - 10^2)/(2*1.8) = 861/3.6 = 239.167 m
2)
30 = 21t - (1/2)(1.8)t^2
0.9t^2 - 21t + 30 = 0
t = (21 - √(441 - 108))/1.8
t = (21 - √333)/1.8
t = 1.5287 s
3)
10*1.5287 = 15.287 m