The equations above can be derived from the fundamental definitions of motion (equations such as a = Δv/Δt). To understand the equations, you need to remember the notation: Δx for displacement, v for velocity and a for acceleration. The subscripts i and f represent initial and final values. We follow a common convention here by using t for elapsed time instead of Δt. We show the equations above and below on the right.

Note that to hold true these equations all require a constant rate of acceleration. Analyzing motion with a varying rate of acceleration is a more challenging task. When we refer to acceleration in problems, we mean a constant rate of acceleration unless we explicitly state otherwise.

To solve problems using motion equations like these, you look for an equation that includes the values you know, and the one you are solving for. This means you can solve for the unknown variable.

In the example problem to the right, you are asked to determine the acceleration required to stop a car that is moving at 12 meters per second in a distance of 36 meters. In this problem, you know the initial velocity, the final velocity (stopped = 0.0 m/s) and the displacement. You do not know the elapsed time. The third motion equation includes the two velocities, the acceleration, and the displacement, but does not include the time. Since this equation includes only one value you do not know, it is the appropriate equation to choose.