1. A particle's motion can be described by the equation s(t) = 3t3 - 6t2 + 2t.

Question

a. When is the particle's velocity in the forward direction?

b. When does the particle go from slowing down to speeding up?

Answer 1

a) The particle's velocity is forward when v(t) >0 v(t) = ds/dt (find the zeroes of the quadratic and you can work out the regions in t where v is greater than zero)

b) Going from slowing down to speeding up means that a(t) > 0 ("smile" or upward curvature). Take dv/dt and find the zero of the linear equation. If the a(t) goes from - to + at that point, that point will answer the question.