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What is Speed and Velocity Help

By — McGraw-Hill Professional
Updated on Oct 25, 2011

Speed

Speed is an expression of the rate at which an object moves, as seen or measured by some stationary observer. But we have to be careful about this. “Stationary” is a relative term. People sitting in an airliner might consider themselves to be “stationary,” but that is not true with respect to the earth! If you stand on a street corner, you might think you are “stationary.” With respect to the earth, you are; with respect to the passengers on an airliner flying high above, you aren’t.

Speed is a Scalar

The standard unit of speed is the meter per second (m/s). A car driving along Route 52 might have a cruise control that you can set at, say, 25 m/s. Then, assuming the cruise control works properly, you will be traveling, relative to the pavement, at a constant speed of 25 m/s. This will be true whether you are on a level straightaway, rounding a curve, cresting a hill, or passing the bottom of a valley. Speed can be expressed as a simple number, and the direction is not important. Speed is a scalar quantity. In this discussion, let’s symbolize speed by the lowercase italic letter v .

Speed can, and almost always does, change with time. If you hit the brakes to avoid a deer crossing the road, your speed suddenly decreases. As you pass the deer, relieved to see it bounding off into a field unharmed, you pick up speed again.

Speed can be considered as an average over time, or as an instantaneous quantity. In the foregoing example, suppose you are driving at 25 m/s and then see a deer, put on the brakes, slow down to a minimum of 10 m/s, watch the deer run away, and then speed up to 25 m/s again, all in a time span of one minute. Your average speed over that minute might be 17 m/s. But your instantaneous speed varies from instant to instant, and is 17 m/s for only two instants (one as you slow down, the other as you speed back up).

How Speed is Determined

In an automobile or truck, speed is determined by the same odometer that measures distance. But instead of simply counting up the number of wheel rotations from a given starting point, a speedometer counts the number of wheel rotations in a given period of time. When the tire circumference is known, the number of wheel rotations in a certain time interval can be translated directly into speed. (But you have to be sure the tires on your car are the right size for the odometer. Otherwise the device will not show the true speed.) In the USA, speed is measured in miles per hour . In the International System it is expressed in kilometers per hour or in meters per second .

Most car and truck speedometers respond almost immediately to a change in speed. These instruments measure the rotation rate of a car or truck axle by another method, similar to that used by the engine’s tachometer (a device that measures revolutions per minute, or rpm). A real-life car or truck speedometer measures instantaneous speed, not average speed. If you want to know the average speed you have traveled during a certain period of time, you must measure the distance on the odometer, and then divide by the time elapsed.

In a given period of time t, if an object travels over a distance d at an average speed v avg , then the following formulas apply. These are all arrangements of the same relationship among the three quantities:

d = v avg t

v avg = d/t

t = d / v avg

Find practice problems and solutions at What is Speed and Velocity Practice Problems.

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