How to Define Acceleration

Acceleration is the rate of change of velocity as a function of time. It is a vector, meaning that it has both magnitude and direction. It is measured in meters per second squared or meters per second (the object's speed or velocity) per second.

In calculus terms, acceleration is the second derivative of position concerning time or, alternately, the first derivative of the velocity concerning time.

Acceleration—Change in Speed

The everyday experience of acceleration is in a vehicle. You step on the accelerator, and the car speeds up as increasing force is applied to the drive train by the engine. But deceleration is also acceleration - the velocity is changing. If you take your foot off the accelerator, the force decreases and velocity is reduced over time. Acceleration, as heard in ads, follows the rule of the change of speed (miles per hour) over time, such as from zero to 60 miles per hour in seven seconds.

Units of Acceleration

The SI units for acceleration are m / s²
(meters per second squared or meters per second per second).

The gal or galileo (Gal) is a unit of acceleration used in gravimetry but is not an SI unit. It is defined as 1 centimeter per second squared. 1 cm/s²

English units for acceleration are feet per second per second, ft/s²

The standard acceleration due to gravity, or standard gravity g₀ is the gravitational acceleration of an object in a vacuum near the surface of the earth. It combines the effects of gravity and centrifugal acceleration from the rotation of the Earth.

Converting Acceleration Units

Newton's Second Law—Calculating Acceleration

The classical mechanic's equation for acceleration comes from Newton's Second Law: The sum of the forces (F) on an object of constant mass (m) is equal to mass m multiplied by the object's acceleration (a).

F = am

Therefore, this can be rearranged to define acceleration as:

a = F/m

The result of this equation is that if no forces are acting on an object (F = 0), it will not accelerate. Its speed will remain constant. If mass is added to the object, the acceleration will be lower. If mass is removed from the object, its acceleration will be higher.

Newton's Second Law is one of the three laws of motion Isaac Newton published in 1687 in Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy). 

Acceleration and Relativity

While Newton's laws of motion apply at speeds we encounter in daily life, once objects are traveling near the speed of light, the rules change. That's when Einstein's special theory of relativity is more accurate. The special theory of relativity says it takes more force to result in acceleration as an object approaches the speed of light. Eventually, acceleration becomes vanishingly small and the object never quite achieves the speed of light.

Under the theory of general relativity, the principle of equivalence says that gravity and acceleration have identical effects. You don't know whether or not you are accelerating unless you can observe without any forces on you, including gravity.