Ok well I'm making a program to solve all my physics formulas quick and easy. But for the equation D = ViT + .5AT^2 I can't solve for T. I forgot some of my algebra 2 skills, which would come in handy here . This is what I have so far:(adsbygoogle = window.adsbygoogle || []).push({});

Since this is somewhat similar to deriving the quadratic equation I wrote that down to try to mirror it.

[tex]d = v_{i}t + \frac{1}{2}at^{2}[/tex]

[tex]0 = v_{i}t + \frac{1}{2}at^{2} - d[/tex]

[tex]\frac{1}{2}at^{2} + v_{i}t - d = 0[/tex]

[tex]\frac{1}{2}at^{2} + v_{i}t = d[/tex]

[tex]t^{2} + \frac{2v_{i}t}{a} = \frac{2d}{a}[/tex]

[tex]t^{2} + \frac{2v_{i}t}{a} + \frac{v_{i}^{2}}{a^{2}} = \frac{2d}{a} + \frac{v_{i}^{2}}{a^{2}}[/tex]

[tex](t + \frac{v_{i}}{a})^{2} = \frac{2d}{a} + \frac{v_{i}^{2}}{a^{2}}[/tex]

[tex]t + \frac{v_{i}}{a} = \sqrt{\frac{2d}{a} + \frac{v_{i}}{a^{2}}}[/tex]

[tex]t = - \frac{v_{i}}{a}\pm\sqrt{\frac{2d}{a} + \frac{v_{i}}{a^{2}}}[/tex]

[tex]t = - \frac{v_{i}}{a}\pm\sqrt{\frac{2da}{a^{2}} + \frac{v_{i}}{a^{2}}}[/tex]

[tex]t = - \frac{v_{i}}{a}\frac{\pm\sqrt{v_{i} + 2ad}}{a}[/tex]

[tex]t = \frac{-v_{i}\pm\sqrt{v_{i} + 2ad}}{a}[/tex]

Is there any way of simlifing this more? Any help is appreciated. Well I can't seem to get my LaTeX image to show up, can anyone edit it so it will?

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# Kinematics: Solve for Time

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