# Speed & Velocity

Velocity has units of distance divided by time. In the lab, we will usually measure velocity in units of m/s. Velocity is also measured in km/h (and even in mi/hr).

If a motorcycle travels 20 m in 2 s, then its average velocity is

If an antique car travels 45 km in 3 h, then its average velocity is

Things do not always move with a constant velocity. The velocity may change. The instantaneous velocity is the velocity "right now", the velocity at some particular moment. We usually shorten that and say simply "the velocity".

This limit is the derivative; that is,

In common, everyday English, "velocity" and "speed" mean the same thing. In Physics, there is a distinction that is sometimes useful.

Velocity is positive if an object is moving to the right and it is negative if an object is moving to the left.

Speed tells how fast an object is moving without saying anything about its direction. Speed is always positive. Speed is the "absolute value" of the velocity. Speed in the velocity information without the sign or direction information.

We can take the definition of average velocity, turn it around, and write

## x = xi + vavg t

where xi = initial position; that is, xi = position at time t = 0

If the velocity is constant, then v = vavg and

## x = xi + v t

In common, ordinary, everyday English the words "speed" and "velocity" mean essentially the same thing. In Physics, "velocity" carries the direction with it. A velocity of v = 100 km/h means it is moving in the positive direction -- usually to the right or up -- while a velocity of v = - 10 m/s means it is moving in the negative direction -- usually to the left or down.

Speed is the absolute value of the velocity or the magnitude of the velocity. Speed is always positive. To tell whether an object is moving to the right or to the left, if you use "speed" you must also specify the direction. You might say that "a car has a speed of 80 km/h, traveling south". You can communicate the same information by saying that "a car has a speed of - 80 km/h".