When an object is moving in a straight-line with constant acceleration, there are a number of standard relationships link velocity, time, displacement and acceleration. It is very important appreciate that these formulae can be used only for motion with constant acceleration. There are many different types of motion in which acceleration is not constant and we must now investigate ways in which the acceleration is not constant and we must now investigate ways in which such motion can be analysed.

We know that velocity is the rate at which displacement varies acceleration is the rate, at which velocity varies, so we can write

and

Further,

These relationships provide the means to solve problems in which the motion varies with time and are equally valid when a, v and s are given in vector form.

Conversely, if we start with the acceleration, then

i.e. if the acceleration of a moving body is a function of time,

velocity can be found by integrating a with respect to t and

displacement can be found by integrating v with respect to t.