after t seconds the position of a particle which is moving along a straight line is x=2t^3-9t^2+12t+6, when is the acceleration zero? determine the velocity at that time.

Answer 1

v = dx/dt = 6 t^2 - 18 t + 12

a = dv/dt = d^2x/dt^2 = 12 t - 18

a is 0 when t = 18/12 = 3/2 = 1.5 seconds

then v = 6(2.25) - 18(1.5) + 12