Deriving The Equations Of Linear Motion With Constant Acceleration

Here is an example of a velocity (v) vs time (t) graph with constant acceleration (a):

The formula for a is:

Final velocity is represented as v_f while initial velocity is represented as v_i. Our first equation of motion is this:

When can rewrite the equation with the v_i being the subject of the formula:

The average velocity (v_avg) can be represented in two ways:

If we equate them, we get our second equation:

Suppose we substitute the first equation into the second one, we can get this:

Or this:

If we simplify, we get our third and fourth equation:

If we make t the subject in the first equation and s the subject in the second equation, then:

If we substitute the first equation into the second one, then:

If we simplify, we get our fifth equation: