Batman was driving the Batmobile at 90 mph (=132 ft/sec), when he sees a brick wall directly ahead. When the Batmobile is 400 feet from the wall, he slams on the brakes, decelerating at a constant rate of 22ft/sec2. Does he stop before he hits the brick wall? If so, how many feet to spare? If not, what is his impact speed? Now the Joker had been driving next to him, also at 90 mph. But the Joker did not hit his brakes as soon as Batman, continuing for 1 second longer than Batman before hitting his brakes, decelerating at a constant rate of 22ft/sec2. How fast is he going when he hits the wall? (Don't worry about Joker - he jettisoned at the last instant, to fight another day!)

Answer 1

distance to stop
Vf^2=Vi^2 + 2ad solve for d.

Answer 2

d^2x/dt^2 = -22

dx/dt = 132 - 22 t

x = Xo + 132 t - (1/2)(22) t^2

so x to stop from 132 ft/s
0 = 132 - 22 t
t = 6 seconds to get dx/dt = 0
then
x = 132 (6) - 11 (36)
x = 792 - 396 = 396 ft to stop
so 4 feet to spare
Now I think you can handle Robin';s unfortunate experience.