Definition: rate of change of position (or distance)

Standard Units: meters/second

## Speed and Velocity

The words speed and velocity are often used interchangeably, but they don’t mean exactly the same thing. Velocity has direction, and so it is a vector. 50 mph northward is a different velocity than 50 mph southward. Speed is merely the magnitude, or numerical value, without regard to direction, so in both these cases the speed is just 50 mph. The speedometer in an automobile measures speed, not velocity, because it doesn’t know in what direction you are going.

Velocity can be a negative number. For example, if the motion is constrained along a line (such as on a straight road), we might define one direction to be positive and the other negative. Speed, on the other hand, is always a positive number (unless it is zero).

The average velocity for a round trip will always be zero, because the net vector displacement is zero. The average speed, of course, will always be a positive number

## Average Velocity This means that if we measure both the distance x and the time t at two different points (point 1 and point 2), then the average velocity is simply the change in distance divided by the time interval.

This formula can be rearranged, with some changes to the symbols, to give

x = x0 + vt

Here x means the position (or distance) right now at time t, x0 means the initial position, and t is the elapsed time. It is important to remember that this formula is only valid if the velocity is constant, because it comes from the formula for average velocity, and the actual velocity is only equal to the average velocity if it is held constant. You could still use this formula if the velocity was not constant, but you would have to use the average velocity for v.

Example: At 10:00 AM your odometer reads 11234 miles. At noon you check it again and it reads 11360 miles. What was your average speed? This does not mean that you were actually going 63 mph. It is only the average. It is possible that you were going much faster than that, but stopped to chat with a friendly highway patrol officer for a while. The 63-mph that we calculated would only be your actual speed if you held your speed constant for the entire two-hour time period.

## Some Speeds

Speed (or velocity) is a distance divided by a time. In the United States speeds are usually measured in miles per hour or feet per second, but in the international standard system of units it is measured in meters per second. Notice that the speed in meters per second is a little less than half of the value in miles per hour.

 Fastest land animal (cheetah): 70 mph 31 m/s Professional fastball pitch or tennis serve 90 mph 40 m/s Commercial Passenger Jet 600 mph 268 m/s Sound (Mach 1) 742 mph 332 m/s Fastest Airplane (SR–71) (Mach 3) 2193 mph 980 m/s Low Earth orbit velocity (Mach 23) 17000 mph 7599 m/s Light 7 ´ 108 mph 3 ´ 108 m/s