Speed and Velocity

In many situations, the word “speed” is used when in fact “velocity” would sometimes be more appropriate. Speed is the rate of change of distance: the word “rate” indicates time, so speed is simply a measure of how much the distance changes in each second of movement. If you took 80 seconds to run 400 m then your speed would be given by 400/80 (distance moved divided by time taken). Your speed would therefore be 5 m/s.

The distance travelled can be in any direction. It doesn’t matter whether you are running in a straight line, and finish at a point that is 400m from the start, or running around a track that brings you back to the same place as where you started. But clearly these are two very different situations.

Velocity is speed in a defined direction – and if the direction changes then the velocity also changes even if the rate of covering distance (speed) stays the same. I strongly suggest that you read the section in italics again as this is vital information in order to understand what follows!

You should recall that speed is a scalar quantity (it has a magnitude but no specific direction) whereas velocity is a vector (it must be specified with a magnitude and a direction). You can read more about scalars and vectors in a previous post (here)

Essentially, velocity is a combination of speed and direction.

If an object is moving in a straight line then its speed and velocity will be the same (because the direction does not change). But if the movement is not in a straight line, then the object’s speed and velocity will share the same magnitude but the direction of its velocity will be changing – and that means its overall velocity is changing even though its speed is staying the same.

This may still be confusing so let’s look at the most common situation that is used to illustrate the important points. Imagine swirling a mass in a circle on the end of a piece of string. If you keep the rate of rotation the same (let’s say it’s one revolution every two seconds, for a medium length piece of string) then the speed stays the same because it always takes two seconds to complete one revolution. But the velocity is constantly changing because the direction of movement is constantly changing.

This leads us to acceleration, which we’ll look in more detail next time. To prepare you for that, here is a quick taster to get you started…

You should already know that if the speed of an object changes then we say it is accelerating (or decelerating). But there can also be acceleration when the speed doesn’t change, such when our mass-on-a-string is being swirled in a circle. How do we know there is acceleration? There are actually two give-aways;

The first reason is that we have to use a force to make the mass go around in a circle. Whenever there is a external force applied to an object, the object will accelerate.

The second reason is because the direction of travel is changing and that means the velocity is changing. Acceleration is defined as the rate of change of velocity.

If you look back to the first paragraph of this article you will see that we have progressed from defining speed (the rate of change of distance) to defining acceleration (the rate of change of velocity) and along the way we have explained the difference between speed and velocity.