Instantaneous Velocity

The velocity and speed of an object are usually variable. We all intuitively understand the concept of instantaneous velocity (or speed). It is what the speedometer reads in a car. Mathematically we define it the same way as we do average velocity or speed except that we make the elapsed time $\Delta$ t $\rightarrow$ 0 , so it is really how far the object goes during a very short period of time. The instantaneous velocity is just called v and, without the aid of calculus, it is given by

The instantaneous velocity is the rate of change of the displacement.

Graphically, v is the slope of the plot of x vs. t. This will be the next topic.

If the velocity does not change (and onlyin this case), then v_av = v.

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