Equations for Uniform Acceleration
Here, we shall learn a few equations that will be useful for calculations involving uniform acceleration.
Lets start with the one we already know:
1. Acceleration = (final velocity - initial velocity) / time taken:
The first new equation we shall derive is:
2. Displacement = average velocity x time
This is obtained using the property that the area under a velocity-time graph is the displacement. Suppose that a body with a velocity u is accelerated uniformly to velocity v over a time t. The velocity-time graph is a straight line, and the area under it is a trapezium.
The area = 1/2 x sum of parallel sides x distance between them = 1/2 x (u + v) x t. This is just the equation above.
The next equation is
3. Displacement = initial velocity x time + half acceleration x time squared
This is obtained by combining the above equations 1 and 2. First, rearrange eq. 1 to give
Next, substitute into eq. 2 like this:
The last equation is
4. Final velocity squared = Initial velocity squared + twice acceleration x displacement
This is again obtained from eqs. 1 and 2, by combining them in a different way. This time, we multiply them directly:
The four equations are summarised here:
1.
Copyright 2010 by Kai Hock. All rights reserved.
Last updated: 28 November 2010.