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176 lines
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HTML
176 lines
7.1 KiB
HTML
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<title>Acceleration</title>
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Acceleration</h1>
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<p><img src="images/hdr-acceleration.jpg" width="100%" alt="dog acceleration" /></p>
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<div id="midul"></div>
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<p>Acceleration is how fast <a href="metric-speed.html">velocity</a> changes:</p>
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<ul>
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<li>Speeding up</li>
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<li>Slowing down (also called <i>deceleration</i>)</li>
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<li>Changing direction</li>
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<li>etc</li>
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</ul>
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<p>It is usually shown as:</p>
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<div class="def">
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<p class="center large"><b>m/s<sup>2</sup></b> <br>
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<i>"meters per second squared"</i></p>
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</div>
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<p>What is this "<b>per second squared</b>" thing? An example will help:</p>
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<div class="example">
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/runner.jpg" width="85" height="161" alt="runner" /></p>
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<h3>A runner accelerates from <b>5 m/s</b> (5 meters per second) to <b>6 m/s</b> <i>in just one second</i></h3>
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<p>So they accelerate by 1 meter per second <b>per second</b></p>
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<p>See how "per second" is used twice?</p>
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<p class="center larger">It can be thought of as (m/s)/s but is usually written m/s<sup>2</sup></p>
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<p>So their acceleration is <b>1 m/s<sup>2</sup></b></p>
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</div>
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<p>The formula is:</p>
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<p class="center large">Acceleration = <span class="intbl">
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<em>Change in Velocity (m/s)</em>
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<strong>Time (s)</strong>
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</span></p>
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<div class="example">
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<h3>Example: A bike race!</h3>
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<p>You are cruising along in a bike race, going a steady <b>10 meters per second</b> (10 m/s).</p>
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<p class="center"><img src="../calculus/images/speed.svg" alt="speed 10m in 1s" /></p>
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<p><b>Acceleration</b>: Now you start cycling faster! You increase to <b>14 m/s</b> over the next 2 seconds (still heading in the same direction):</p>
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<p class="center"><img src="../calculus/images/acceleration.svg" alt="acceleration from 10m per 1s to 14m per 1s" /></p>
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<p>Your velocity <b>increases by 4 m/s</b>, over a time period of <b>2 seconds</b>, so:</p>
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<p class="center large">Acceleration = <span class="intbl">
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<em>Change in Velocity (m/s)</em>
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<strong>Time (s)</strong>
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</span></p>
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<p class="center large">= <span class="intbl">
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<em>4 m/s</em>
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<strong>2 s</strong>
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</span> = 2 m/s<sup>2</sup></p>
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<p>Your speed changes by <b>2 meters per second</b> <i>per second</i>.<br></p>
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</div>
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<div class="example">
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<h3>Example: You are running at 7 m/s, and skid to a halt in 2 seconds.</h3>
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<p>You went from 7 m/s to 0, so that is a decrease in speed:</p>
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<p class="center large">Acceleration = <span class="intbl">
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<em>Change in Velocity (m/s)</em>
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<strong>Time (s)</strong>
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</span></p>
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<p class="center large">= <span class="intbl">
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<em>−7 m/s</em>
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<strong>2 s</strong>
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</span> = −3.5 m/s<sup>2</sup><br></p>
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</div>
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<p>We don't always say it, but acceleration has <b>direction</b> (making it a <a href="../algebra/vectors.html">vector</a>):</p>
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<div class="example">
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<p style="float:left; margin: 0 10px 5px 0;"> </p>
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<h3>A car is heading <b>West at 16 m/s</b>.<br>
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<img style="float:left; margin: 0 10px 5px 0;" src="images/car-turn.jpg" width="400" height="130" alt="car turn" /><br>
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The driver flicks the wheel, and within 4 seconds has the car headed <b>East at 16 m/s</b>.
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<div style="clear:both"></div>
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What is the acceleration?</h3>
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<p>The numbers are the same, but the direction is different!</p>
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<p class="center large">Acceleration = <span class="intbl">
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<em>Change in Velocity (m/s)</em>
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<strong>Time (s)</strong>
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</span></p>
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<p class="center large">Acceleration = <span class="intbl">
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<em>From 16 m/s West to 16 m/s East</em>
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<strong>4 s</strong>
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</span></p>
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<p>From 16 m/s West to 16 m/s East is a total change of 32 m/s towards the East.</p>
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<p class="center large">Acceleration = <span class="intbl">
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<em>32 m/s East</em>
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<strong>4 s</strong>
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</span> = 8 m/s<sup>2</sup> East</p>
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</div>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="../algebra/images/vector-add.svg" alt="vector add" /></p>
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<p> </p>
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<p>For more complicated direction changes read <a href="../algebra/vectors.html">vectors</a>.</p>
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<p> </p>
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