Derivation of the Equations of Motion

Start with:

then:

Combine these two equations to get:

This is Equation 3 in the

discussion that follows.

From the definition of acceleration:

This is Equation 1.

Solve this equation for t:

Put this result in the 3^rd equation from the top:

This is Equation 2.

Take the 4^th equation down and use it to replace v in the 3^rd equation down:

This is Equation 4.