# 4.01 Equations of motion

In this section we will use a velocity time graph to derive four standard equations of motion that can be applied to objects moving in one dimension with constant acceleration.
After completing this section you should be able to:

• Derive the four equations for motion
• Use these equations to solve problems involving motion in one dimension with constant acceleration

Equation 1
The area under a velocity time graph is equal to the object's displacement

We can see that if the triangular section indicated in the diagram was repositioned it would form a rectangle with sides of length (v+u)/2 and t. The area of this square is equal to (v+u)/2 x t Therefore the displacement of the object is given by the equation

s = (v + u)/2 x t      (eq. 1)

(Note the term (v + u)/2 represents the average velocity for a uniformly accelerating object. Therefore the equation is simply stating that the displacement is equal to the average velocity multiplied by the time the object has been moving)