PhysicsLAB: Derivation of the Kinematics Equations for Uniformly Accelerated Motion

This derivation is based on the properties of a velocity-time graph for uniformly accelerated motion where the

Equation #1: slope = acceleration

Starting with the slope

where

gives us our first equation:

In this equation

a represents the object's uniform acceleration
t represents the time interval over which the object's velocity changed
v_f represents the object's final velocity at the end of the time interval
v_o represents the object's initial velocity at the beginning of the time interval

Equation #2: rearrange equation #1 for v_f

Equation #3: area = displacement

Equation #4: multiply equation #1 by equation #3

Equation #1:

Equation #3:

Equation #5: substitute equation #2 into equation #3

Equation #2:

Equation #3:

EQUATION SUMMARY (these MUST be memorized)