Batman was driving the Batmobile at 90 mph (=132 ft/sec), when he sees a brick w

Question

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/sec.
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/sec.
How fast is he going when he hits the wall? (Don't worry about Joker - he jettisoned at the last instant,to fight for another day!)

Explanation / Answer

Given initial velocity of batmobile,u=132 ft/sec

decelaration=-a=22ft/sec2

so a= -22ft/sec2

at the time t when batmobile stops velocity v=0

u+at=0

132-22t=0

22t=132

t=132/22 = 6seconds

distance covered by bat mobile in 6 second is S=ut+(1/2)at2

S=132(6)+(0.5)(-22)(6)2 =396 ft

since the wall is 400 ft ahead,bat mobile didnt hit it

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