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<!DOCTYPE html>
<html data-require="math kinematics">
<head>
<title>Kinematic Equations</title>
<script src="../khan-exercise.js"></script>
</head>
<body>
<div class="exercise">
<div class="vars">
<var id="MOTION">randFromArray([ randomConstantMotion, randomFreefallMotion, randomFreefallMotion, randomAccelMotion, randomAccelMotion, randomAccelMotion ])()</var>
<var id="OMITTED">MOTION.omitted</var>
<var id="UNKNOWN">MOTION.unknown</var>
</div>
<div class="problems">
<div>
<div class="problem">
<p data-if="'d' !== OMITTED && 'd' !== UNKNOWN"><code>d = <var>u(MOTION, "d")</var></code></p>
<p data-if="'v_i' !== OMITTED && 'v_i' !== UNKNOWN"><code>v_i = <var>u(MOTION, "v_i")</var></code></p>
<p data-if="'v_f' !== OMITTED && 'v_f' !== UNKNOWN"><code>v_f = <var>u(MOTION, "v_f")</var></code></p>
<p data-if="'a' !== OMITTED && 'a' !== UNKNOWN"><code>a = <var>u(MOTION, "a")</var></code></p>
<p data-if="'t' !== OMITTED && 't' !== UNKNOWN"><code>t = <var>u(MOTION, "t")</var></code></p>
<p><code><var>OMITTED</var> = ?</code></p>
<p><code><var>UNKNOWN</var> = ?</code></p>
</div>
<div class="question">
<p>Solve for <code><var>UNKNOWN</var></code>. Round to the nearest tenth.</p>
<p>Make sure you select the proper units. You may do arithmetic with a calculator.</p>
</div>
<p class="solution"><var>roundTo(1, MOTION[UNKNOWN])</var></p>
</div>
</div>
<div class="hints">
<div data-if="OMITTED === 'd'">
<p><code>v_f = v_i + at</code></p>
<div data-if="UNKNOWN === 'v_f'">
<p><code>v_f = <var>u(MOTION,"v_i")</var> + (<var>u(MOTION,"a")</var>)(<var>u(MOTION,"t")</var>)</code></p>
<p><code>v_f = <var>u(MOTION,"v_f")</var></code></p>
</div>
<div data-if="UNKNOWN === 'v_i'">
<p><code>v_f - at = v_i</code></p>
<p><code><var>u(MOTION,"v_f")</var> - (<var>u(MOTION,"a")</var>)(<var>u(MOTION,"t")</var>) = v_i</code></p>
<p><code><var>u(MOTION,"v_i")</var> = v_i</code></p>
</div>
<div data-if="UNKNOWN === 'a'">
<p><code>\frac{v_f - v_i}{t} = a</code></p>
<p><code>\frac{<var>u(MOTION,"v_f")</var> - <var>u(MOTION,"v_i")</var>}{<var>u(MOTION,"t")</var>} = a</code></p>
<p><code><var>u(MOTION,"a")</var> = a</code></p>
</div>
<div data-if="UNKNOWN === 't'">
<p><code>\frac{v_f - v_i}{a} = t</code></p>
<p><code>\frac{<var>u(MOTION,"v_f")</var> - <var>u(MOTION,"v_i")</var>}{<var>u(MOTION,"a")</var>} = t</code></p>
<p><code><var>u(MOTION,"t")</var> = t</code></p>
</div>
</div>
<div data-if="OMITTED === 'v_i'">
<p><code>d = v_f t - \frac{1}{2}at^2</code></p>
<div data-if="UNKNOWN === 'd'">
<p><code>d = (<var>u(MOTION,"v_f")</var>)(<var>u(MOTION,"t")</var>) - \frac{1}{2}(<var>u(MOTION,"a")</var>)(<var>u(MOTION,"t")</var>)^2</code></p>
<p><code>d = <var>u(MOTION,"d")</var></code></p>
</div>
<div data-if="UNKNOWN === 'v_f'">
<p><code>\frac{d + \frac{1}{2} at^2}{t} = v_f</code></p>
<p><code>\frac{<var>u(MOTION,"d")</var> + \frac{1}{2}(<var>u(MOTION,"a")</var>)(<var>u(MOTION,"t")</var>)^2}{<var>u(MOTION,"t")</var>} = v_f</code></p>
<p><code><var>u(MOTION,"v_f")</var> = v_f</code></p>
</div>
<div data-if="UNKNOWN === 'a'">
<p><code>\frac{d - v_f*t}{-\frac{1}{2}t^2} = a</code></p>
<p><code>\frac{<var>u(MOTION,"d")</var> - (<var>u(MOTION,"v_f")</var>)(<var>u(MOTION,"t")</var>)}{-\frac{1}{2}(<var>u(MOTION,"t")</var>)^2} = a</code></p>
<p><code><var>u(MOTION,"a")</var> = a</code></p>
</div>
<div data-if="UNKNOWN === 't'">
<p><code>0 = -\frac{1}{2}a*t^2 + v_f*t - d</code></p>
<div>
<p>By the quadratic formula:</p>
<p><code>t = \frac{ -v_f +- \sqrt{ v_f^2 - 2ad } }{-a}</code></p>
</div>
<p><code>t = (-<var>u(MOTION,"v_f")</var> +- sqrt((<var>u(MOTION,"v_f")</var>)^2 - 2(<var>u(MOTION,"a")</var>)(<var>u(MOTION,"d")</var>)))/(-<var>u(MOTION,"a")</var>)</code></p>
<p><code>t = <var>u(MOTION,"t")</var></code></p>
</div>
</div>
<div data-if="OMITTED === 'v_f'">
<p><code>d = v_i t + \frac{1}{2}at^2</code></p>
<div data-if="UNKNOWN === 'd'">
<p><code>d = (<var>u(MOTION,"v_i")</var>)(<var>u(MOTION,"t")</var>) + \frac{1}{2}(<var>u(MOTION,"a")</var>)(<var>u(MOTION,"t")</var>)^2</code></p>
<p><code>d = <var>u(MOTION,"d")</var></code></p>
</div>
<div data-if="UNKNOWN === 'v_i'">
<p><code>\frac{d - \frac{1}{2}at^2}{t} = v_i</code></p>
<p><code>\frac{<var>u(MOTION,"d")</var> - \frac{1}{2}(<var>u(MOTION,"a")</var>)(<var>u(MOTION,"t")</var>)^2}{<var>u(MOTION,"t")</var>} = v_i</code></p>
<p><code><var>u(MOTION,"v_i")</var> = v_i</code></p>
</div>
<div data-if="UNKNOWN === 'a'">
<p><code>\frac{d - v_i t}{\frac{1}{2} t^2} = a</code></p>
<p><code>\frac{<var>u(MOTION,"d")</var> - (<var>u(MOTION,"v_i")</var>)(<var>u(MOTION,"t")</var>)}{\frac{1}{2}(<var>u(MOTION,"t")</var>)^2} = a</code></p>
<p><code><var>u(MOTION,"a")</var> = a</code></p>
</div>
<div data-if="UNKNOWN === 't'">
<p><code>0 = \frac{1}{2} at^2 + v_i t - d</code></p>
<div>
<p>By the quadratic formula:</p>
<p><code>t = \frac{ -v_i +- \sqrt{v_i^2 + 2ad} }{a}</code></p>
</div>
<p><code>t = \frac{-<var>u(MOTION,"v_i")</var> +- sqrt((<var>u(MOTION,"v_i")</var>)^2 + 2(<var>u(MOTION,"a")</var>)(<var>u(MOTION,"d")</var>))}{<var>u(MOTION,"a")</var>}</code></p>
<p><code>t = <var>u(MOTION,"t")</var></code></p>
</div>
</div>
<div data-if="OMITTED === 'a'">
<p><code>d = \frac{1}{2}(v_i + v_f)t</code></p>
<div data-if="UNKNOWN === 'd'">
<p><code>d = \frac{1}{2}(<var>u(MOTION,"v_i")</var> + <var>u(MOTION,"v_f")</var>)(<var>u(MOTION,"t")</var>)</code></p>
<p><code>d = <var>u(MOTION,"d")</var></code></p>
</div>
<div data-if="UNKNOWN === 'v_i'">
<p><code>\frac{2d}{t} - v_f = v_i</code></p>
<p><code>\frac{2(<var>u(MOTION,"d")</var>)}{<var>u(MOTION,"t")</var>} - <var>u(MOTION,"v_f")</var> = v_i</code></p>
<p><code><var>u(MOTION,"v_i")</var> = v_i</code></p>
</div>
<div data-if="UNKNOWN === 'v_f'">
<p><code>\frac{2d}{t} - v_i = v_f</code></p>
<p><code>\frac{2(<var>u(MOTION,"d")</var>)}{<var>u(MOTION,"t")</var>} - <var>u(MOTION,"v_i")</var> = v_f</code></p>
<p><code><var>u(MOTION,"v_f")</var> = v_f</code></p>
</div>
<div data-if="UNKNOWN === 't'">
<p><code>\frac{2d}{v_i + v_f} = t</code></p>
<p><code>\frac{2(<var>u(MOTION,"d")</var>)}{<var>u(MOTION,"v_i")</var> + <var>u(MOTION,"v_f")</var>} = t</code></p>
<p><code><var>u(MOTION,"t")</var> = t</code></p>
</div>
</div>
<div data-if="OMITTED === 't'">
<p><code>v_f^2 = v_i^2 + 2ad</code></p>
<div data-if="UNKNOWN === 'd'">
<p><code>\frac{v_f^2 - v_i^2}{2a} = d</code></p>
<p><code>\frac{(<var>u(MOTION,"v_f")</var>)^2 - (<var>u(MOTION,"v_i")</var>)^2}{2(<var>u(MOTION,"a")</var>)} = d</code></p>
<p><code><var>u(MOTION,"d")</var> = d</code></p>
</div>
<div data-if="UNKNOWN === 'v_i'">
<p><code>+-\sqrt{v_f^2 - 2ad} = v_i</code></p>
<p><code>+-\sqrt{(<var>u(MOTION,"v_f")</var>)^2 - 2(<var>u(MOTION,"a")</var>)(<var>u(MOTION,"d")</var>)} = v_i</code></p>
<p><code><var>u(MOTION,"v_i")</var> = v_i</code></p>
</div>
<div data-if="UNKNOWN === 'v_f'">
<p><code>v_f = +-\sqrt{v_i^2 + 2ad}</code></p>
<p><code>v_f = +-\sqrt{(<var>u(MOTION,"v_i")</var>)^2 + 2(<var>u(MOTION,"a")</var>)(<var>u(MOTION,"d")</var>)}</code></p>
<p><code><var>u(MOTION,"v_f")</var> = v_f</code></p>
</div>
<div data-if="UNKNOWN === 'a'">
<p><code>\frac{v_f^2 - v_i^2}{2d} = a</code></p>
<p><code>\frac{(<var>u(MOTION,"v_f")</var>)^2 - (<var>u(MOTION,"v_i")</var>)^2}{2(<var>u(MOTION,"d")</var>)} = a</code></p>
<p><code><var>u(MOTION,"a")</var> = a</code></p>
</div>
</div>
</div>
</div>
</body>
</html>
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