A particle in rectilinear motion follows the path s(t) = t^3 − 6t^2 + 9t, where s is in meters, and t is in seconds.

Question

A particle in rectilinear motion follows the path s(t) = t³ − 6t² + 9t, where s is in meters, and t is in seconds.

Answer 1

zeros are 0 and 3

s'= 3t^2 -12t +9=0

divide by 3

t^2 -4t +3=0 =(t-3)(t-1) t=1, 3

which divides into time intervals where it changes direction

from forward to backwards and backwards to forwards