The Derivative as a Rate of Change. Suppose that a particle moves along a coordinate line in such a way that its position is described by the function s(t) = 413 – 10t2 + 7t + 3 for 0<t<3. Find the particle's velocity as a function of t: v(t) = Determine the open intervals on which the particle is moving to the right and to the left: Moving right on: Moving left on: Find the particle's acceleration as a function of t: a(t) = Determine the open intervals on which the particle is speeding up and slowing down: Slowing down on: Speeding up on: NOTE: State the open intervals as a comma separated list (if needed).