I'm self-studying Calc 1 for Engineers, and here's the question:
Suppose a particle is moving along a straight line and its position with respect to a reference point is $s=4\cdot t^3-8\cdot t^2+3\cdot t+2$, where $s$ is in meters and $t$ is in seconds.
A) Find the velocity and acceleration as functions of $t$.
B) Find the acceleration after 1 second.
C) Find the acceleration at the instance(s) when the velocity is 0.
I'm not sure how to define velocity and acceleration as functions in this context, though. Previously, in Physics, I was taught that velocity is distance divided by time; however, since we're dealing with rate of change, I assume the process is different. I tried researching the equations to use, but results varied: some suggested I take the limit of the function, others simply just repeated the distance/time thing, etc. I'm just not sure where to start. Parts B and C should be self-explanatory once I can figure out part A, though; B is just substitution, and C refers to points of inflection (I assume).
I saw another thread on here referring to a similar question, and perhaps I misunderstood the answers, but it also sounded like velocity is just the derivative of the function, and acceleration is the derivative of velocity.