Equations for Speed, Velocity & Acceleration

By Peter Flom; Updated April 24, 2017
Velocity is a composite of speed and direction.

Speed, velocity and acceleration are all concepts relating to the relationship between distance and time. Intuitively, it may seem that speed and velocity are synonyms, but there is a difference. That difference means that it is possible to travel at a constant speed and always be accelerating.

Formula for Speed

Speed is the amount of distance traveled divided by the amount of time taken. It is expressed in units of distance per time; this could be miles per hour, kilometers per second, inches per year or any distance unit per any time unit. For example, if you travel 50 miles in one hour, your speed is 50 mph (miles per hour).

Formula for Velocity

Velocity is a vector; that is, it involves both speed and direction. It is reported in the same units as speed, but with a direction added, for instance, 40 miles per hour west. To calculate it, find your starting point and ending point, find the distance between them, then find the direction.

Formula for Acceleration

Acceleration is the change in velocity. It is expressed in units of distance per unit of time per unit of time; often the latter is abbreviated to unit of time, squared. For example, if you accelerate at 10 meters per second squared, it means that your velocity changes at a rate of 10 meters per second each second. To calculate it, subtract your velocity at the beginning from your velocity at the end, and divide by the amount of time. For instance, if you start at zero velocity (standing still) and 10 seconds later you are moving east at 10 meters per second, your velocity is

10 meters per second/10 seconds = 1 meter per second squared.

Constant Speed, Constant Acceleration

How can you accelerate constantly while being at a constant speed? If you travel in a circle, without speeding up or slowing down, your velocity changes each second, and, therefore, you are accelerating without changing your speed. For example, if you run at 10 miles per hour along a circle that is 10 miles long, and you start off facing north and running clockwise, then, after 2 1/2 minutes, you have a velocity of 2.5 miles per hour northeast, or 0.0417 miles per minute northeast (because 2.5/60 = 0.0417). You have an acceleration of (0.0417 miles per minute northeast)/2.5 = 0.0167 miles per minute per minute.

About the Author

Peter Flom is a statistician and a learning-disabled adult. He has been writing for many years and has been published in many academic journals in fields such as psychology, drug addiction, epidemiology and others. He holds a Ph.D. in psychometrics from Fordham University.