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class="breadcrumb"> <li><a href="../../../physics.html"><i class="fa fa-home"></i></a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../217/mechanics.html">Mechanics</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../218/kinematics.html">Kinematics</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">Distance and displacement</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 15 minutes"><i class="fa fa-clock-o"></i> 15'</span> </ol> <article id="main-article"> <p><img alt="" src="../../mechanics/kin-2-s.jpg" style="float: left; width: 250px; height: 167px;">We all know that when we move, we cover a distance. Distances are part of our daily lives in getting around school, playing sport and travel. But what if we walk in a complete circle? We've moved through a distance but overall have returned to where we started. </p> <p>This page will show how to add vectors, or to resolve a vector into two perpendicular components. You might need to revisit <a href="../188/pythagoras-and-trigonometry.html" title="Pythagoras and trigonometry">Pythagoras and trigonometry</a> first. </p> <hr class="hidden-separator"> <div class="panel panel-turquoise panel-has-colored-body"> <div class="panel-heading"> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <p>Distance is a scalar quantity and displacement is a vector quantity.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/160106594"></iframe></div> <p><img alt="" height="121" src="../../screen-shot-2016-11-01-at-20.04.01.png" style="float: left;" width="132"><em>Displacement</em> is a vector quantity, which means it has magnitude and direction, unlike its scalar equivalent <em>distance </em>(see <a href="../232/vectors.html" title="Vectors">Vectors</a>). This makes it possible for a body to move through a distance without having an overall displacement.</p> <hr class="hidden-separator"> <div class="magenta"> <p>Displacement should be represented by an arrow, not just a line. Defining a <em>positive direction </em>is also important. Let's say that up and right are positive directions; a displacement down and to the left would have a negative value.</p> </div> <p>A 2-dimensional displacement can be represented by vectors. Added nose to tail, the original vector is the resultant.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/160106549"></iframe></div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <div> <div class="panel panel-yellow panel-has-colored-body panel-has-border"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Taking components</p> </div> </div> <div class="panel-body"> <div> <p>It is possible to resolving (split) a displacement vector into horizontal and vertical components. This is a useful technique when horiztonal and vertical motion can be treated independently, such as <a href="../227/projectile-motion.html" title="Projectile motion">Projectile motion</a>.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/200784833"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-yellow panel-has-colored-body panel-has-border panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Adding perpendicular components</p> </div> </div> <div class="panel-body"> <div> <p>Use <a href="../188/pythagoras-and-trigonometry.html" title="Pythagoras and trigonometry">Pythagoras</a>' theorem to add together perpendicular vectors.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/160106585"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-purple"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Summary</p> </div> </div> <div class="panel-body"> <div> <p>This Geogebra animation demonstrates how we can represent the motion of a particle using a displacement-time graph to show how the gradient and sign of the line relates to the direction and velocity of the particle.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/160106565"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test Yourself</p> </div> </div> <div class="panel-body"> <div> <p><i>Use quizzes to practise application of theory.</i> </p> <br><a class="btn btn-primary btn-block text-center" data-toggle="modal" href="#991fa682"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="991fa682"> <div class="modal-dialog" style="width: 95vw; max-width: 960px"> <div class="modal-content"> <div class="modal-header slide-quiz-title"> <h4 class="modal-title" style="width: 100%;"> Displacement and distance <strong class="q-number pull-right"> <span class="counter">1</span>/<span class="total">1</span> </strong> </h4> </div> <div class="modal-body p-xs-3"> <div class="slide-quiz" data-stats="6-33-221" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question"><p>A body travels along the path shown</p><p style="text-align: center;"><img alt="" src="../../images/dispq1.png" style="width: 322px; height: 288px;"></p><p>Fill in the following quantities</p></div><div class="q-answer"><p>Distance travelled <input type="text" style="height: auto;" data-c="7"> <span class="review"></span>m (1sf)</p><p>Magnitude of displacement <input type="text" style="height: auto;" data-c="5"> <span class="review"></span> m</p><p>Displacement East <input type="text" style="height: auto;" data-c="4"> <span class="review"></span> m</p><p>Displacement North <input type="text" style="height: auto;" data-c="3"> <span class="review"></span>m </p></div><div class="q-explanation"><p>The distance travelled is an estimate.<br>The triangle made by the components is a 345 triangle</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The animation shows the motion of a blue dot.</p><p style="text-align: center;"><img alt="" class="gifffer" data-gifffer="/media/physics/images/displq2.gif" style="width: 440px; height: 344px;"></p></div><div class="q-answer"><p>Fill in values for the displacement from starting point at the following times</p><p>0s <input type="text" style="height: auto;" data-c="0"> <span class="review"></span></p><p>2s <input type="text" style="height: auto;" data-c="4W"> <span class="review"></span> with direction (NSEW)</p><p>4s <input type="text" style="height: auto;" data-c="0"> <span class="review"></span></p><p>10s <input type="text" style="height: auto;" data-c="0"> <span class="review"></span></p><p>Taking π to be 3, estimate the distance travelled at the following times</p><p>2s <input type="text" style="height: auto;" data-c="6"> <span class="review"></span></p><p>4s <input type="text" style="height: auto;" data-c="12"> <span class="review"></span></p><p>8s <input type="text" style="height: auto;" data-c="18"> <span class="review"></span></p><p>10s <input type="text" style="height: auto;" data-c="24"> <span class="review"></span></p></div><div class="q-explanation"><p>The circumference = 2πr = 12 (approximating π to 3)</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The following blue dot only moves in 1 dimension</p><p style="text-align: center;"><img alt="" class="gifffer" data-gifffer="/media/physics/images/displq.gif" style="width: 440px; height: 212px;"></p></div><div class="q-answer"><p>Enter the values for the displacement from the original position at the following times (no units):</p><p>3s <input type="text" style="height: auto;" data-c="3"> <span class="review"></span></p><p>4s <input type="text" style="height: auto;" data-c="5"> <span class="review"></span></p><p>6s <input type="text" style="height: auto;" data-c="0"> <span class="review"></span></p><p>Enter the values for distance travelled at these times:</p><p>3s <input type="text" style="height: auto;" data-c="3"> <span class="review"></span></p><p>4s <input type="text" style="height: auto;" data-c="5"> <span class="review"></span></p><p>6s <input type="text" style="height: auto;" data-c="10"> <span class="review"></span></p><p>Enter the values for the displacement from the origin at the following times:</p><p>0s <input type="text" style="height: auto;" data-c="-3"> <span class="review"></span></p><p>3s <input type="text" style="height: auto;" data-c="0"> <span class="review"></span></p><p>4s <input type="text" style="height: auto;" data-c="2"> <span class="review"></span></p><p>6s <input type="text" style="height: auto;" data-c="-3"> <span class="review"></span></p></div><div class="q-explanation"><p>Left is negative right is positive</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Observe the motion of the blue dot and deduce which of the graphs represents the motion.</p><p style="text-align: center;"><img alt="" class="gifffer" data-gifffer="/media/physics/images/displ4.gif" style="width: 308px; height: 184px;"></p><p style="text-align: center;"> </p><p style="text-align: center;"><img alt="" src="../../images/dispq2.png" style="width: 400px; height: 342px;"></p></div><div class="q-answer"><p><label class="radio" style=" float: left; margin-right: 40px; "><input class="c" type="radio"> D</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> A</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> B</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> C</label></p></div><div class="q-explanation"><p>+ displacement followed by -<br>The end part is the fastest so steepest.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div> </div> </div> <div class="modal-footer slide-quiz-actions"> <div class=""> <div class="pull-left pull-xs-none mb-xs-3"> <button class="btn btn-default d-xs-none btn-prev"> <i class="fa fa-arrow-left"></i> Prev </button> </div> <div class="pull-right pull-xs-none"> <button class="btn btn-success btn-xs-block text-xs-center btn-results" style="display: none"> <i class="fa fa-bar-chart"></i> Check Results </button> <button class="btn btn-default d-xs-none 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