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I understand that the equation used to find the equation used to find displacement when the initial velocity is unknown is:

$vt-(at^2)/2$

how would you rearrange this to solve for $t\;?$ When I try I get $t$ on both sides of the equation.

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2 Answers 2

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You can rearrange using the quadratic formula to get: $$ t = \frac{-u±\sqrt(u^2+2as)}{a} $$ Thanks AccidentalFourierTransform for the answer.

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The equation used to find the displacement in motion with constant acceleration in 1 dimension is -

$ s = ut + \frac{a{t}^{2}}{2} $

where u is the initial velocity , s is displacement and a is acceleration (constant).

You can re-write the equation as -

$ t^2 + \frac{2u}{a}t - \frac{2s}{a} = 0 $

or $ (t + \frac{u}{a})^2 - \frac{2s}{a} - \frac{u^2}{a^2} = 0 $

$ (t + \frac{u}{a})^2 = \frac{u^2 + 2sa}{a^2} $

$ t + \frac{u}{a} = \pm\frac{\sqrt{u^2 + 2sa}}{|a|} $

So, $ t = - \frac{u}{a} \pm\frac{\sqrt{u^2 + 2sa}}{|a|} $

(You can get the same result by using the quadratic formula.)

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  • $\begingroup$ The OP specified that $u$, the initial velocity is unknown... $\endgroup$
    – DJohnM
    Jan 24, 2016 at 16:17

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