# Acceleration

## Definition

**Acceleration**, the second derivative of displacement, is defined to be the change of velocity per unit time at a certain instance.

A common misconception is that acceleration implies a POSITIVE change of velocity, while it could also mean a NEGATIVE one.

## Formula for Acceleration

Let be the velocity of an object at a time and be the velocity of the same object at a time . If acceleration, , is known to be constant, then Note that velocity is a vector, so the magnitudes cannot be just subtracted in general.

If acceleration is not constant, then we can treat velocity as a function of time, . Then, at a particular instance,

## Useful Formulae

Position and its time derivatives are often used in kinematics. For example, the following four equations relate the position , velocity , and (constant) acceleration by magnitude: By the chain rule, one can also show Lastly, we have the famous formula of Newton relating the force and acceleration experienced by a massive object:

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