Time Independent Acceleration Algebra

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Here we will take a look at the equation that allows us to solve for several quantities when the object is accelerating. This particular equation is time independent; that is, time does not appear in the equation. The equation looks like this:

velocity final squared minus velocity original squared equals two times acceleration times displacement

This equation would read:

Final velocity squared minus original velocity squared equals two times acceleration times displacement.

We will use algebra to solve the above equation for each of its variables.

 

The equation in its original form is not solved for any individual quantity:

time independent kinematics equation

 

Here, we will solve for final velocity, vf:

equation algebra Start here.
equation algebra Add vo2 to each side.
equation algebra Take the square root of each side.

 

Here, we will solve for original velocity, vo:

equation algebra Start here.
equation algebra Subtract vf2 from each side.
equation algebra Multiply each side by (-1).
equation algebra Take the square root of each side.

 

Now, let's solve for displacement, d:

equation algebra Start here.
equation algebra Divide each side by 2a.
equation algebra Rearrange by switching the left and right sides.

 

Lastly, let's solve for acceleration, a:

equation algebra Start here.
equation algebra Divide each side by 2d.
equation algebra Rearrange by switching left and right sides.

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