Find the velocity,acceleration ,rest and moving forward and backwards

Question

The position of a particle is given as s(t) = 2/5t^5 −2t^4 + 2t^3 where t is in hours and s(t) is in miles.

Find the velocity of the particle.
Find the acceleration of the particle
When is the particle at rest?
When is the particle moving forward?
When is the particle moving backward?

Answer 1

s=⅖t⁵-2t⁴+2t³

v=ds/dt=2t⁴-8t³+6t² (velocity)

a=dv/dt=8t³-24t²+12t (acceleration)

ds/dt=0 when stationary:

2t²(t²-4t+3)=2t²(t-1)(t-3)=0 stationary at t=0, 1, 3.

Moving forward when v>0, so t>3.

Moving backward when 1<t<3.