Question 1175915
velocity is ds/dt=2t^4-8t^3+6t^2
acceleration is d^2s/dt^2=8t^3-24t^2+12t
at rest when the velocity is 0
moving forward with v>0
backward with v<0.
0=2t^2(t^2-4t+3)=2t^2((t-1)(t-3))
so at t=1 sec and t=3 sec it is at rest.
when t is 2 seconds, the function ds/dt is negative, so it is moving backward. After 3 seconds, it is moving forward, and before 1 second it is moving forward.

{{{graph(300,300,-10,10,-10,10,2x^4-8x^3+6x^2,.4x^5-2x^4+2x^3)}}}