Question
The one-dimensional displacement, s meters of a particle, after t seconds, is given by the function s=t(t-4)^2.
(i) when does the particle have zero acceleration?
(ii) where is the particle at this time and what is it doing?
(i) when does the particle have zero acceleration?
(ii) where is the particle at this time and what is it doing?
Answers
Reiny
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
= 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