Physics Kinematics Equation Must Be Solved W/ Algebra

**jessegarwood** · August 9th 2010, 06:53 PM

So I have the formula and values substituted in correctly - but now the simple algebra part is killing me.
x = vt + 1/2at^2
.06=(2*10^3)t + 1/2(4*10^7)t^2

What is t?

**eumyang** · August 9th 2010, 07:09 PM

$.06 = (2*10^3)t + 1/2(4*10^7)t^2$
$.06 = 2000t + 20000000t^2$

Set equal to 0 and rearrange:
$20000000t^2 + 2000t - 0.06 = 0$

Use the quadratic formula:
$\begin{aligned} t &= \dfrac{-2000 \pm \sqrt{2000^2 - 4(20000000)(-0.06)}}{2(20000000)} \\ &= \dfrac{-2000 \pm \sqrt{4000000 + 4800000}}{40000000} \\ &= \dfrac{-2000 \pm \sqrt{8800000}}{40000000} \\ &\approx 2.42 \times 10^{-5}, -1.24 \times 10^{-4} \end{aligned}$

**TKHunny** · August 9th 2010, 07:11 PM

Yikes! You should have studied Quadratic Equations over the previous years.

If you write it like this: ½at^2 + vt - x = 0, you should find solutions from the Quadratic Equation, or Completing the Square. Ringing any bells, yet?

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