# Average and Instantaneous Velocity **Average Velocity:** Let $s(t)$ be a position function of an object moving along a coordinate axis at time $t$. The average velocity of the object over a time $[a, t]$, where $a<t$: $v_{ave}=\frac{s(t)-s(a)}{t-a}$ This function looks similar to the slope formula > [!Definition] > For a function $s(t)$, the instantaneous velocity at time $t=a$ is the value that the average velocities approach on the interval $[a,t]$ as $a$ and $t$ get closer to each other. **Instantaneous Velocity** The **instantaneous velocity** is the value ![[velocity.png]]