Equations of Motion

Equation 1

If we start with the equation for acceleration we can rearrange this to give us an equation 1

Equation 2

We start with the definition of velocity and rearrange for displacement

velocity = displacement / time displacement = velocity x time

In situations like the graph to the right the velocity is constantly changing, we need to use the average velocity.

displacement = average velocity x time

The average velocity is give by: average velocity =

We now substitute this into the equation above for displacement

displacement = x time

Equation 3

With Equations 1 and 2 we can derive an equation which eliminated v. To do this we simply substitute into

This can also be found if we remember that the area under a velocity-time graph represents the distance travelled/displacement. The area under the line equals the area of rectangle A + the area of triangle B.

Area = Displacement = s = since then so the equation becomes which then becomes equation 3

Equation 4

If we rearrange equation 1 into which we will then substitute into equation 2:

Any question can be solved as long as three of the variables are given in the question.

Write down all the variables you have and the one you are asked to find, then see which equation you can use.

These equations can only be used for motion with UNIFORM ACCELERATION.