Instantaneous Quantities

Speed and Velocity

The instantaneous velocity is just that, the velocity at a given instant. If we take average velocities over shorter and shorter time intervals, the velocity we find will eventually approach the instantaneous velocity.

Instantaneous Velocity (usually denoted as v) = lim?t->0(?x/?t) = dx/dt (in calculus notation)

Instantaneous speed (s) = |v|

Thus, v has both a magnitude and a direction, making it a generally more useful quantity. In 1D the direction is either positive or negative, denoting motion towards “higher” or “lower” values of x respectively. Conventionally (but by no means always), the higher xs lie to the right and the lower xs lie to the left.

Typically in physics, we measure speed (and velocity) in quantities like m/s, but in the outside world, other quantities like miles/hour are common. It is important to practice the techniques of unit conversion discussed in chapter two.