**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 = x**_{i} + v_{avg} t

**where x**_{i} = initial position; that is, x_{i}
= position at time t = 0

**If the velocity is constant, then v = v**_{avg} and

**x = x**_{i} + 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".

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(c) Doug Davis, 2001; all rights reserved