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# Speed and Velocity

by Ron Kurtus (18 July 2014)

If the separation between you—as an observer—and another object in space changes, that object is considered in motion with respect to you. If you observe the separation between two objects changing, one or both objects are considered in motion with respect to each other, as well as with respect to you.

The relative speed of an object is the distance it travels in a given time with respect to you or some stationary object. Often, the ground is considered the stationary object.

When traveling a certain distance, the speed of the object may vary over that distance. Thus the calculation is the average speed. The speed at a given instance is called the instantaneous speed.

Velocity is the speed of the object in a specific direction. Since a direction is involved, velocity can be expressed geometrically as a vector quantity.

Questions you may have include:

• What is relative speed?
• What is instantaneous speed?
• What is velocity?

This lesson will answer those questions. Useful tool: Units Conversion

## Relative speed

The speed of an object is always with respect to another object that is considered a point of reference. That object can seem to be stationary or moving relative to something else.

For example, when you are standing near a road, your speed with respect to the ground is zero. But an automobile passing by has a speed with respect to you and the road.

A person sitting in the car has a zero speed with respect to the car. But he sees you as moving backward with respect to him at some speed.

## Average and instantaneous speed

The speed of an object is the distance it travels over a period of time. This is actually the average speed, since the distance may be large. The distance traveled can even be on a curved path. That can be written as:

s = x/t

where

• s is the speed
• x is the distance traveled
• t is the elapsed time

Note: We use x as distance instead of d to avoid confusion with the derivative of distance, as is seen below.

The instantaneous speed is when the distance traveled approaches zero. That can be written as:

s = dx/dt

where

• dx is the derivative of x
• dt is the derivative of t

## Velocity

Velocity is the speed of an object in a given direction. It can be represented graphically as a vector.

Average velocity is defined as the displacement for a given time period. Displacement is the movement from point A to point B in a straight line.

Instantaneous velocity is

The instantaneous velocity is when the displacement approaches zero. That can be written as:

v = dx/dt

where

• dx is the derivative of x in a specific direction
• dt is the derivative of t

## Summary

If you observe the separation between two objects changing, one or both objects are considered in motion with respect to each other, as well as with respect to you.

The relative speed of an object is the distance it travels in a given time with respect to you or some stationary object. Often, the ground is considered the stationary object.

When traveling a certain distance, the speed of the object may vary over that distance. Thus the calculation is the average speed. The speed at a given instance is called the instantaneous speed.

Velocity is the speed of the object in a specific direction. Since a direction is involved, velocity can be expressed geometrically as a vector quantity.

Move quickly

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