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281 lines
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<title>Speed and Velocity</title>
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<script>reSpell=[["meters","metres"],["kilometers","kilometres"]];</script>
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<meta name="description" content="Learn the difference between Speed and Velocity (they are different!)" />
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Speed and Velocity</h1>
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<h2>Speed and Velocity</h2>
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<p>Speed is how fast something moves.</p>
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<p >Velocity is speed with a <b>direction</b>.</p>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="../images/art/ariel-run-ball.jpg" width="180" height="134" alt="ariel running with ball" /></p>
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<p> </p>
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<p>Saying Ariel the Dog runs at <b>9 km/h</b> (kilometers per hour) is a speed.</p>
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<p>But saying he runs <b>9 km/h Westwards</b> is a velocity.</p>
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<p> </p>
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<div style="clear:both"></div>
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<div class="simple">
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<table style="border: 0; margin:auto;">
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<tr>
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<th> </th>
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<th width="200" align="center">Speed</th>
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<th width="200" align="center">Velocity</th>
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</tr>
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<tr>
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<td><b>Has:</b></td>
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<td align="center"><b>magnitude</b></td>
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<td align="center"><b>magnitude</b> and <b>direction</b></td>
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</tr>
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<tr>
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<td>Example:</td>
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<td align="center">60 km/h</td>
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<td align="center">60 km/h North</td>
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</tr>
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<tr>
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<td>Example:</td>
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<td align="center">5 m/s</td>
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<td align="center">5 m/s upwards</td>
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</tr>
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</table>
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</div>
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<p>Imagine something moving back and forth very fast: it has a high speed, but a low (or zero) velocity.</p>
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<h2>Speed</h2>
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<p>Speed is measured as distance moved over time.</p>
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<p class="center large">Speed = <span class="intbl">
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<em>Distance</em>
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<strong>Time</strong>
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</span></p>
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<div class="example">
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<h3>Example: A car travels 50 km in one hour.</h3>
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<p>Its average speed is 50 km per hour (50 km/h)</p>
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<p class="center larger">Speed = <span class="intbl">
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<em>Distance</em>
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<strong>Time</strong>
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</span> = <span class="intbl">
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<em>50 km</em>
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<strong>1 hour</strong>
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</span></p>
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</div>
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<p>We can also use these symbols:</p>
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<p class="center large">Speed = <span class="intbl">
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<em>Δs</em>
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<strong>Δt</strong>
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</span></p>
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<p>Where Δ ("<i>Delta</i>") means "change in", and</p>
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<ul>
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<li><b>s</b> means distance ("s" for "space")</li>
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<li><b>t</b> means time</li>
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</ul>
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<div class="example">
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<p style="float:right; margin: 0 0 5px 10px;"><img src="../data/images/runners.jpg" width="200" height="177" alt="runners" /></p>
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<h3>Example: You run 360 m in 60 seconds.</h3>
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<div class="tbl">
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<div class="row"><span class="left"><span class="center large">Speed = </span></span><span class="right"><span class="center large"><span class="intbl">
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<em>Δs</em>
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<strong>Δt</strong>
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</span></span></span></div>
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<div class="row"><span class="left"><span class="center large">= </span></span><span class="right"><span class="center large"><span class="intbl">
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<em>360 m</em>
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<strong>60 seconds</strong>
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</span></span></span></div>
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<div class="row"><span class="left"><span class="center large">= </span></span><span class="right"><span class="center large"><span class="intbl">
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<em>6 m</em>
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<strong>1 second</strong>
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</span></span></span></div>
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</div>
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<p>So your speed is 6 meters per second (6 m/s).</p>
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</div>
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<h2>Units</h2>
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<p>Speed is commonly measured in:</p>
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<ul>
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<li>meters per second (m/s or m s<sup>-1</sup>), or</li>
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<li>kilometers per hour (km/h or km h<sup>-1</sup>)</li>
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</ul>
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<p>A km is 1000 m, and there are 3600 seconds in an hour, so we can convert like this (see <a href="unit-conversion-method.html">Unit Conversion Method</a> to learn more):</p>
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<p class="center larger"><span class="intbl">
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<em>1 m</em>
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<strong>1 s</strong>
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</span> × <span class="intbl hi">
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<em>1 km</em>
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<strong>1000 m</strong>
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</span> × <span class="intbl hi">
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<em>3600 s</em>
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<strong>1 h</strong>
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</span> = <span class="intbl">
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<em>3600 <span style="text-decoration:line-through">m</span> · km · <span style="text-decoration:line-through">s</span></em>
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<strong>1000 <span style="text-decoration:line-through">s</span> · <span style="text-decoration:line-through">m</span> · h</strong>
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</span> = <span class="intbl">
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<em>3.6 km</em>
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<strong>1 h</strong>
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</span></p>
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<p>So <b>1 m/s is equal to 3.6 km/h</b></p>
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<div class="example">
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<h3>Example: What is 20 m/s in km/h ?</h3>
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<p class="center larger">20 m/s × <span class="intbl">
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<em>3.6 km/h</em>
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<strong>1 m/s</strong>
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</span> = 72 km/h</p>
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</div>
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<div class="example">
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<h3>Example: What is 120 km/h in m/s ?</h3>
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<p class="center larger">120 km/h × <span class="intbl">
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<em>1 m/s</em>
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<strong>3.6 km/h</strong>
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</span> = 33.333... m/s</p>
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</div>
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<h2>Average vs Instantaneous Speed</h2>
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<p>The examples so far calculate <b>average speed</b>: how far something travels over a period of time.</p>
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<p>But speed can change as time goes by. A car can go faster and slower, maybe even stop at lights.</p>
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<p class="center"><img src="images/car-journey-speed.svg" alt="car journey speed average and instantaneous" /></p>
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<p>So there is also <b> instantaneous speed</b>: the speed at an <b>instant</b> in time. We can try to measure it by using a very short span of time (the shorter the better).</p>
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<div class="example">
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<h3>Example: Sam uses a stopwatch and measures 1.6 seconds as the car travels between two posts 20 m apart. What is the <b> instantaneous speed</b>?</h3>
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<p>Well, we don't know exactly, as the car may have been speeding up or slowing down during that time, but we can estimate:</p>
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<p class="center larger"><span class="intbl">
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<em>20 m</em>
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<strong>1.6 s</strong>
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</span> = 12.5 m/s = 45 km/h</p>
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<p>It is really still an average, but is close to an instantaneous speed.</p>
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</div>
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<h2>Constant Speed</h2>
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<p>When the speed does not change it is <b>constant</b>.</p>
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<p>For constant speed, the average and instantaneous speeds are the same.</p>
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<h2>Velocity</h2>
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<p>Velocity is speed with a <b>direction</b>.</p>
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<p class="center">It is actually a <a href="../algebra/vectors.html">vector</a> ...<br>
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<img src="../algebra/images/vector-mag-dir.svg" alt="vector magnitude and direction" /><br>
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... as it has magnitude <b>and</b> direction</p>
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<p>Because the direction is important velocity uses <b>displacement</b> instead of distance:</p>
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<div class="defImgLt"></div>
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<p class="center"><img src="images/displace-distance.svg" alt="displacement vs distance" /></p>
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<p class="center large">Speed = <span class="intbl">
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<em>Distance</em>
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<strong>Time</strong>
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</span></p>
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<p class="center large">Velocity = <span class="intbl">
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<em>Displacement</em>
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<strong>Time</strong>
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</span> in a direction.</p>
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<div class="example">
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<h3>Example: You walk from home to the shop in 100 seconds, what is your speed and what is your velocity?</h3>
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<p class="center"><img src="images/shop-trip.svg" alt="shopping trip" /></p>
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<p class="center larger">Speed = <span class="intbl">
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<em>220 m</em>
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<strong>100 s</strong>
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</span> = 2.2 m/s</p>
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<p class="center larger">Velocity = <span class="intbl">
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<em>130 m</em>
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<strong>100 s</strong>
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</span> East = 1.3 m/s East</p>
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<h3>You forgot your money so you turn around and go back home in 120 more seconds: what is your round-trip speed and velocity?</h3>
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<p>The total time is 100 s + 120 s = 220 s:</p>
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<p class="center larger">Speed = <span class="intbl">
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<em>440 m</em>
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<strong>220 s</strong>
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</span> = 2.0 m/s</p>
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<p class="center larger">Velocity = <span class="intbl">
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<em>0 m</em>
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<strong>220 s</strong>
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</span> = 0 m/s</p>
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<p>Yes, the velocity is zero as you ended up where you started.</p>
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</div>
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<p>Learn more at <a href="../algebra/vectors.html">Vectors</a>.</p>
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<h2>Relative</h2>
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<p>Motion is relative. When we say something is "at rest" or "moving at 4 m/s" we forget to say "in relation to me" or "in relation to the ground", etc.</p>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/earth-rotate.gif" width="128" height="128" alt="earth rotating" /></p>
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<p>Think about this: are you really standing still? You are on planet Earth which is spinning at 40,075 km per day (about 1675 km/h or 465 m/s), and moving around the Sun at about 100,000 km/h, which is itself moving through the Galaxy.</p>
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<p>Next time you are out walking, imagine you are still and it is the world that moves under your feet. Feels great.</p>
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<p><b>It is all relative!</b></p>
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<p> </p>
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<div class="questions">
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<script>getQ(11893, 11894, 11895, 11896, 11897, 11898, 11899, 11900, 11901, 11902);</script>
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</div>
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<div class="related">
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<a href="metric-system.html">Metric System</a>
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<a href="index.html">Measurement Index</a>
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</div>
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Copyright © 2020 MathsIsFun.com
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