The one-dimensional displacement, s meters of a particle, after t seconds, is given by the function s=t(t-4)^2.

Question

(i) when does the particle have zero acceleration?

(ii) where is the particle at this time and what is it doing?

Answer 1

s = t(t^2 - 8t + 16)
= t^3 - 8t^2 + 16t

v = 3t^2 - 16t + 16
a = 6t - 16

for zero of a,
6t-16=0
t = 16/6 = 8/3 seconds

when t = 8/3
v = 3(64/9) - 16(8/3) + 16
= -16/3
s = (8/3)(8/3 - 4)^2 = 128/27

work these answers in with your concluding statements