Finding the third equation

Finding the third major equation.

This last equation deals exclusively with finding velocities without a stopwatch. It's especially useful when your just playing around with numbers and are curious to see how fast something went. In reality, you'll never use it anywhere except a physics lab because you will need acceleration, distance traveled, and initial velocity, which is too hard to do at home. Anywho, here's how you find it:

First you'll want to solve V_f=at+V_i for t. Here's what that would look like starting with the V sub f equation.

V_f-V_i=at
t=(V_f-V_i)/a

Now take this equation and put it the second equation for t. Then simplify the expresion. This will look like this: (I suggest doing this on your own because this will look really confusing on your browser.)

1) x_f=1/2a((V_f-V_i)/a)²+V_i((V_f-V_i)/a)+x_i
2) x_f=1/2a((V_f²-2V_fV_i+V_i²)/a²)+((V_iV_f-V_i²)/a)+x_i
3) x_f=((V_f²-2V_fV_i+V_i²)/2a)+(2/2)((V_iV_f-V_i²)/a)+(2a/2a)x_i
4) x_f=((V_f²-2V_fV_i+V_i²)/2a)+((2V_iV_f-2V_i²)/2a)+((2ax_i)/2a)
5) x_f=((V_f²-V_i²)/2a)+x_i
6) x_f-x_i=(V_f²-V_i²)/2a
7) 2a(x_f-x_i)=V_f²-V_i²
8) V_f²=2a(x_f²-x_i²)+V_i²

Now you may have simplified it differently, but you should end up with the same basic equation. This is your third and final main equation. Congradulations, you are now ready to move onto the practice problems. If you are daring, you can go deriving the first two equations using calculus. If you aren't in calculus, then I wouldn't recommend this. However, to solidify your understanding of these equations, I would suggest looking at other equations that can be found. These can be helpful when trying to solve the practice problems.