4.03 Equations of motion

Equation 3
As stated before the area under the graph represents displacement
We have already shown that s = (v+u)/2 x t

velocity time graph

Another way of representing the area under the graph is to split it into two sections;
A rectangular section with area = base x height
and a triangular section with area = 1/2 x base x height

This gives us the equation s = ut + 1/2(v-u)t

From equation 2 we know that a = (v-u)/t and therefore (v-u) = at
Therefore we can substitute the term (v-u) in the above equation for at
This gives;

s = ut + 1/2 at2     (eq. 3)

[i.e. total displacement = displacement due to initial velocity plus addition displacement due to the objects acceleration]