# Velocity, Speed

We can think of the*velocity vector*in terms of a speedometer reading with units [meters/second = m/s] and a direction. The magnitude of the velocity vector (that is, just the speedometer reading) is called

*speed*. The word "velocity" is sometimes used to refer to the vector and sometimes to the magnitude. When in doubt, you should assume it refers to the vector.

If an object is traveling such that its velocity vector is constant, we say it is in

*uniform motion*. An example is a car going a constant 30 m/s (freeway speed) west. We can write the following equations for uniform motion in one dimension:

(1a)

(1b)

When you see a formula in this text, instead of speeding by it, slow down and look at it. Ask yourself, "What is this equation telling me?" Equation (1a) is just another form of "distance equals rate times time" for an object in uniform motion. Since

*v*is constant, this tells you, for instance, that a car will travel twice as far if it travels for twice the time. This makes sense.Equation (1b) is like the first, only Î”

*x*is replaced by its definition*x*_{2}â€“*x*_{1}. Do you see why it is this and not*x*_{1}â€“*x*_{2}or*x*_{2}+*x*_{1}?But in some problems the velocity does change, and we must pay attention to several velocities, that is,
and
The average velocity is defined as

*v*_{1}initial velocity,*v*_{2}final velocity,*v*_{avg}average velocity. (2)

This is different from equation (1). Equation (2) is the definition of an average velocity over a time interval when velocity is changing, whereas equation (1) defines a constant velocity and only holds for time intervals when the motion is uniform.

Example

A car goes west at 10 m/s for 6 s, then it goes north at 10 m/s for 5 s, and then it goes west again at 4 m/s for 15 s. What are *v*_{1}, *v*_{2}, and *v*_{avg}?

Solution

Well, we have *v*_{1} = 10 m/s and *v*_{2} = 4 m/s. For the average velocity we need to DRAW A DIAGRAM (Figure 2-6). The Pythagorean theorem gives us Î”*s* = 130 m.

Thus *v*_{avg} = 130m/26s = 5 m/s

Figure 2-6