In physics, acceleration is speeding up, slowing down, or changing direction. Acceleration contrasts with uniform velocity, that is, unchanging velocity. A car driving along at 80 miles down a perfectly straight Nevada highway, would be traveling at uniform velocity—not accelerating at all. Or, if the car sat parked under the shade of a giant cactus, it would also be at uniform velocity—zero miles per hour.
In physics, both speeding up and slowing down are called “acceleration.” Speeding up is called “positive acceleration” and slowing down is “negative acceleration.” The term “deceleration,” the common English word for slowing down, is not used in physics.
If, while flying along at 80 miles an hour, the driver swerves to miss a desert tortoise, that’s acceleration. And, of course, slowing down to the speed limit when a patrol car pulls into view, that’s acceleration, too. Speeding up again when the patrol car goes out of sight? Again, that’s acceleration.
Acceleration mostly occurs when starting and ending motion. On Earth, acceleration in the sense of speeding up, usually occurs for a brief period when beginning to move. Acceleration, in the sense of slowing down, usually occurs for brief time when ending movement. Once a certain velocity is attained, it is usually more or less maintained. This is true of walking for example. One starts out stationary, gains speed, and then maintains that speed until reaching the destination or pausing to rest.
In some situations on Earth, acceleration does occur a good deal of the time, for example in stop-and-go traffic or when traveling in a curved path or a path with many changes of direction.
Measurement of acceleration. Acceleration is measured in meters per second per second. This is written: (m/s2).
A car that is accelerating might drive one meter per second faster than it did the previous second:
• Start (standing still) – drives 0 meters per second.
• End of the first second – drives 1 meter per second.
• End of second – drives 2 meters per second.
• End of the third second – drives 3 meters per second.
This is acceleration at the rate of one meter per second per second or 1 m/s/s or 1 m/s2.
How to find acceleration mathematically. If one knows the velocity of an object, one can find its acceleration at any moment in time by taking the derivative of its velocity. Of course, one would need to know calculus also so that one could take the derivative.
If one knows physics and the force and mass of an object, one can use a version of Newton’s Second Law of Motion (Acceleration = Force divided by Mass or a=F/m) to find its acceleration. All one would need is algebra. The version of this equation that we usually see is: F = ma; a=F/m is a simple rewrite of this equation.