Velocity in Math: Definition, Equation & Problems

What Is Velocity?

Velocity is defined as the rate of travel of an object, along with its direction. Velocity tells you how fast an object is moving as well as in what direction it is moving. It is similar to speed, except that it also adds direction. So, while speed is directionless, velocity is directional speed.

Speed Vs. Velocity

Speed only gives you a number that tells you how fast you are going. Velocity, because it adds direction, tells you how fast you are changing your position. Because of this difference, if your position doesn’t change even if you are moving very fast, your velocity will be zero. If you were to run in place very fast, your speed may be six mph, but your velocity would be zero because you aren’t going anywhere. If you were to run backwards and forwards, always returning to your same spot, your velocity would be zero again because you didn’t go anywhere.

So remember that for velocity, your position needs to change, but for speed it doesn’t. You can go as fast as you can in the same spot without gaining any velocity. But if you are moving forward in a particular direction, then you would be gaining velocity. For velocity, you need to be moving somewhere; you can’t be stationary.

Equation for Velocity

The equation or formula for velocity is similar to speed.

To figure out velocity, you divide the distance by the time it takes to travel that same distance, then you add your direction to it. For example, if you traveled 50 miles in 1 hour going west, then your velocity would be 50 miles/1 hour westwards, or 50 mph westwards.

Calculating Velocity

Calculating velocity is a lot like calculating speed, with the addition of taking into account the direction in which you are moving. In order to figure out velocity, your problem would have to allow you to calculate the speed along with what direction the object is moving in. Without the directional information, you can’t calculate velocity.