What is the difference between speed and velocity?

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Speed is defined as the rate of change of motion of an object. In other words, it is the ratio of distance traveled to time taken.

speed = distance traveled by the object / time taken for the journey

In comparison, velocity is the rate of change of position of...

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Speed is defined as the rate of change of motion of an object. In other words, it is the ratio of distance traveled to time taken.

speed = distance traveled by the object / time taken for the journey

In comparison, velocity is the rate of change of position of an object. In other words, it is the ratio of displacement to the time taken by an object.

Velocity = displacement of the object / time taken

Speed is a scalar quantity and only has a magnitude. In comparison, velocity is a vector quantity and has both magnitude and direction. 

Speed is dependent on the path taken by the object, since it is needed to determine the distance. Velocity is independent of the path taken by an object, since it depends on the displacement (distance between initial and final position of an object).

Hope this helps.

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Many people use the terms more or less interchangeably (often using "velocity" when they mean "speed" but want to sound more impressive), but there is a very simple but vital difference between the two.

The easiest way to explain the difference between speed and velocity is that speed is a number, while velocity is a vector. Speed is the magnitude of velocity.

Speed has no direction associated with it; it's just a value, like 50 m/s or 60 mph.

But velocity has a direction, and is generally expressed in one of two forms: Components in x, y, and z, like this:
<30 m/s, 40 m/s, 0 m/s>

or magnitude and direction, like this:
50 m/s at 53 degrees north of east.

I've chosen these so they are in fact the same vector. This is analogous to the difference between rectangular (Cartesian) coordinates and polar coordinates.

Speed is the magnitude of direction; the above velocity vector has a magnitude of 50 m/s, so the speed is 50 m/s.

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The speed of an object can be calculated if you know the distance that was traveled divided by the time it took to get there. Units can be miles per hour or kilometer per hour for example. However, velocity is the measurement of the rate and direction of change of a given object in motion. For instance, if a person is running 2 miles per hour, that is her speed. However, if she is running 2 miles per hour southwest, that is her velocity.

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