ACCELERATION

Acceleration is the measurement of how quickly the velocity of an object is changing, usually with respect to time. If you measure the velocity of an object at a particular time (Time₁), then again at a subsequent time (Time₂), then the average acceleration which the object has experienced will be:

Acceleration = (Velocity₂ - Velocity₁) / (Time₂-Time₁)

Clearly, the longer the period of time over which the measurements are taken, the more that value becomes an average, and the less will be known about the instantaneous acceleration of the object.

Acceleration is a critically important value for dynamic systems, because it is the instantaneous acceleration imposed on moving (dynamic) components, along with the mass of the components, which determines the actual forces raquired or applied in order to get components within the a system to change velocity from one value to another (Newton's second law), 

Linear acceleration is typically expressed in inches-per-second-per-second and feet-per-second-per-second(velocity per unit time). Common units of angular acceleration are degrees-per-second-per-second, radians-per-second-per-second and RPM-per-second.

However, acceleration (and velocity as well) need not be expressed with respect to time. For example, the acceleration value typically used in camshaft lobe design is inches-per-degree-per-degree or inches-per-degree² . This value is the acceleration which a cam lobe applies to the cam follower it is driving. In order to calculate the forces a cam applies to its mating components, the cam lobe angular velocity with respect to time must be known. Using that value, the lobe acceleration value can then be converted into inches-per-second-per-second, from which the forces are then calculated. In 2004, for some undiscernible, but most certainly politically-correct, reason, the cam design community apparently switched to metric units { velocity in mm/deg and lobe acceleration in mm/deg² }.