SOLUTION: 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 pa

Question 1175915: 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 by Boreal(15235) (Show Source): You can put this solution on YOUR website!
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.

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