The position s(t) of an object moving along a straight line is given. Find object's velocity and acceleration and all times where acceleration is 0.
s(t) = 3t^5 - 5t^3 - 7
velocity = s'(t) = 15t^4 - 15t^2
acceleration = s''(t) = 60t^3 - 30t
0=60t^3 - 30t
0=30t(2t^2 -1)
0=t and
0=2t^2 - 1
1=2t^2
1/2 = t^2
square root of 1/2 = t
Hmmmm....I doubt the last part.