A train is travelling at 32 ms. The driver brakes, producing a deceleration of k716-tms after / seconds. The train comes to rest in 16 seconds. Find k, and how far the train travel before coming to rest.

Answer 1

v = at + c, where a is the acceleration and c is a constant
when t = 0, v = 32, so 32 = 0 + c
v = at + 32
when t = 16, v = 0
0 = 16a + 32
a = -2

so we have
a = -2 m/s^2
v = -2t + 32
s = -t^2 + 32t + k, where s is the distance in metres
distance between t= 0 and t = 16
= (0 + 0 + k) - (-16^2 - 512 + k)
= 768