Acceleration - Definition and Properties

Definition and Properties

Mathematically, instantaneous acceleration—acceleration over an infinitesimal interval of time—is the rate of change of velocity over time:

i.e., the derivative of the velocity vector as a function of time.

(Here and elsewhere, if motion is in a straight line, vector quantities can be substituted by scalars in the equations.)

Average acceleration over a period of time is the change in velocity divided by the duration of the period

Acceleration has the dimensions of velocity (L/T) divided by time, i.e., L/T2. The SI unit of acceleration is the metre per second per second (m/s2); this can be called more meaningfully "metre per second per second", as the velocity in metres per second changes by the acceleration value, every second.

An object moving in a circular motion—such as a satellite orbiting the earth—is accelerating due to the change of direction of motion, although the magnitude (speed) may be constant. When an object is executing such a motion where it changes direction, but not speed, it is said to be undergoing centripetal (directed towards the center) acceleration. Oppositely, a change in the speed of an object, but not its direction of motion, is a tangential acceleration.

Proper acceleration, the acceleration of a body relative to a free-fall condition, is measured by an instrument called an accelerometer.

In classical mechanics, for a body with constant mass, the (vector) acceleration of the body is proportional to the net force vector (i.e., sum of all forces) acting on it (Newton's second law):

where F is the resultant force acting on the body, m is the mass of the body, and a is its acceleration. As speeds approach that of light in a vacuum, relativistic effects become increasingly large and acceleration becomes less.