# How do I find velocity and acceleration as functions of t?

May 2, 2018

It depends on the nature of the motion you're studying. For example, if a body moves with constant velocity, you will have $v = \frac{s}{t}$, and $a = 0$.
On the other hand, if a body moves with constant acceleration, you will have $v = a t$ and $a = k$ (some constant).
In general, the only thing you can say is that, if you know the function $s \left(t\right)$ that gives the position $s$ at every time $t$, you will have that the velocity is the first derivative of $s$, and the acceleration the second derivative.