Acceleration

In the same way that the velocity is the rate of change of the displacement, the acceleration is defined as the rate of change of the velocity:

\[\rm a = \frac{\Delta v}{\Delta t} \]
as $\Delta$t $\rightarrow$0

Just like the velocity and displacement, the acceleration is also a vector.

The concept of average velocity leads directly to average acceleration. If an object begins with velocity v₀ and ends with velocity v, then the average acceleration is given by:

\[\rm a_{av} = \frac{v-v_0}{t-t_0} \]

For most of the following chapters we will deal only with problems in which the acceleration is a constant. In this case (and only in this case), we have

a = a_av.

If the acceleration is not constant, then calculus is needed to describe the motion of the bodies. If it is constant, then all the kinematic equations are just algebraic.