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# Physics and Speed Help

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By McGraw-Hill Professional
Updated on Sep 4, 2011

## Introduction to Speed

Speed is an expression of the rate at which an object moves relative to some defined reference point of view. The reference frame is considered stationary , even though this is a relative term. A person standing still on the surface of the Earth considers himself or herself to be stationary, but this is not true with respect to the distant stars, the Sun, the Moon, or most other celestial objects.

## 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 device that you can set at, say, 25 m/s. Then, assuming that 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. Thus speed is a scalar quantity. In this discussion, let’s symbolize speed by the lowercase italic letter v .

Speed can, of course, change with time. If you hit the brakes to avoid a deer crossing the road, your speed will decrease suddenly. 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 that you are moving along at 25 m/s and then see the 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 1 minute. Your average speed over that minute might be 17 m/s. However, 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. However, 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. Knowing the wheel circumference, the number of wheel rotations in a certain time interval can be translated directly into meters per second.

You know, of course, that most 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. In fact, 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 displacement of magnitude q at an average speed v avg , then the following formulas apply. These are all arrangements of the same relationship among the three quantities.

q = v avg t

v avg = q / t

t = q / v avg

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