Motion With Constant Acceleration

This section refers to the special case of rectilinear motion in which the acceleration is constant. In cases where the acceleration is constant, a(t) can be represented simply by the constant a, and both velocity and position can be found by using the following formulas:

v(t)=v0 + at  
s(t)=s0 + v0t + at2  

Where v0 is the initial velocity at time t = 0 and s0 is the initial position at time t = 0. Note that these formulas are in compliance with the relations v(t) = s'(t) and a(t) = v'(t).

A ball dropped vertically from a height travels in this fashion, because it is accelerated by gravity at a constant rate of 9.8 meters per second per second.