Instantaneous Velocity

Definition:

$$\vec{v}$$ = $$\lim_{\Delta t \rightarrow 0}^{}$$$${\frac{\Delta \vec{r}}{\Delta t}}$$

 

Figure 3.3: Instantaneous velocity in 2-D.

Interpretation: When $\Delta$t $\rightarrow$ 0, the point Q in the figure gets closer and closer to the point P and the direction of $\Delta$$\vec{r}$ approaches the direction of a tangent to the curve at point P. Thus the instantaneous velocity $\vec{v}$ is parallel to the tangent and in the same direction as the motion.