Question

The path of a particle moving in a straight line is given by s=t³-6t²+9t+4 find s and a when v=0

Answer 1

ds/dt = v = 3 t^2 - 12 t + 9

d^2s/dt^2 = 6 t - 12 = a

when v = 0
3 t^2 - 12 t + 9 = 0
t^2 - 4 t + 3 = 0
(t - 3) (t-1) = 0
so
when t = 1 and when t = 3 , v = 0
when t = 1
s = 1 - 6 + 9 + 4 = 8
a = 6 - 12 = -6
when t = 3
s = 27 - 54 + 27 + 4 = 4
a = 18-12 = 6