# Equation to isolate time

1. Dec 9, 2008

### rigory

1. The problem statement, all variables and given/known data
For quite a while I have been working on this equation and attempting to isolate time, however i have so far been unable to do so.

2. Relevant equations
D=VoT+1/2AT^2

3. The attempt at a solution
I've been going through and keep coming up with T on both sides of the equation. I'd very much appreciate any help in this area.

2. Dec 9, 2008

3. Dec 9, 2008

### Gregg

Re: Kinematics

to isolate time in $s=vt+1/2at^2$

$$1/2AT^2 + VoT - D = 0$$

a=1/2A
b=Vo
c=-D

$$X = \frac{-b + \sqrt{b^2 - 4ac}}{2a}$$

we get

$$T = \frac{-Vo + \sqrt{(Vo)^2 - 4(1/2A)(-D)}}{2(1/2A)}$$

Last edited: Dec 9, 2008
4. Dec 9, 2008

### rigory

Re: Kinematics

thanks, i think that will work, i've been trying to program it into a graphing calculator, but couldnt find a way to get it.

5. Dec 9, 2008

### fluidistic

Re: Kinematics

Well you're lucky enough Gregg did all the job for you. (By the way it's forbidden according to the forum's rules).
You really should learn how to find roots of any quadratic function. This is a not so hard thing to accomplish and very useful. (Don't use calculator if possible.)