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fa-star-o"></i></a> </h1> <ol 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">Equations of uniformly accelerated motion</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 30 minutes"><i class="fa fa-clock-o"></i> 30'</span> </ol> <article id="main-article"> <p><img alt="" src="../../mechanics/kin-4-s.jpg" style="float: left; width: 250px; height: 167px;"></p> <p>On this page we will consider the <em>suvat</em> equations in turn.</p> <hr class="hidden-separator"> <div class="panel panel-has-colored-body panel-turquoise"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <div> <p>The <em>suvat</em> equations apply to uniform motion, which means <strong>constant or zero acceleration</strong>.</p> <p>More complicated motion can be analysed by splitting it into steps that are so small we can assume the acceleration is constant. For example, a vehicle travelling at 10 m s<sup>-1</sup> and then 15 m s<sup>-1</sup> could be considered in two stages.</p> </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-has-colored-body panel-has-border panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Deriving <span class="math-tex">\(s={(u+v)\over2}t\)</span></p> </div> </div> <div class="panel-body"> <div> <p>This equation is derived by equating the two expressions for average velocity, <span class="math-tex">\(v_{av}={s \over t}\)</span> and <span class="math-tex">\(v_{av}={(u+v)\over2}\)</span>..</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/160349705"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Deriving <span class="math-tex">\(s=ut+{1\over2}at^2\)</span></p> </div> </div> <div class="panel-body"> <div> <p>This equation is derived by using the definition of acceleration, <span class="math-tex">\(a={(v-u)\over t} \Rightarrow t={(v-u)\over a}\)</span> to substitute for <em>t</em> in the previous equation.</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/160350534"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-has-border panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Deriving <span class="math-tex">\(v^2=u^2+2as\)</span></p> </div> </div> <div class="panel-body"> <div> <p>This time the equation <span class="math-tex">\(a={(v-u)\over t}\)</span> is used to substitute for <em>v</em> in the expression <span class="math-tex">\(s={(u+v)\over2} t\)</span></p> <div class="smart-object center" data-id="212" style="text-align: center;"> <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/160351418"></iframe></div> </div> </div> </div> <div class="panel-footer"> <div> </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><em>Here is a recap of the equations so far.</em></p> <p style="text-align: center;"><img alt="" src="../../images/flashcard-images/suvat.png" style="width: 137px; height: 200px;"></p> </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="#62e9f1ed"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="62e9f1ed"> <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%;"> suvat (deciding which) <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="6-138-222" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question"><p>A ball rolls down a 30° slope starting from rest.</p><p>To calculate the velocity after 5s I would use</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> s = (u + v)t/2</label></p><p><label class="radio"><input type="radio"> s = ut + 1/2 at<sup>2</sup></label></p><p><label class="radio"><input class="c" type="radio"> a = (v - u)/t</label></p><p><label class="radio"><input type="radio"> v<sup>2</sup> = u<sup>2</sup> +2as</label></p></div><div class="q-explanation"><p>we don't know s but do know v (0ms<sup>-1</sup>), a (gsin30°) and t</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>A car accelerates from 5 ms<sup>-1</sup> to 10 ms<sup>-1</sup> in 10 s</p><p>To calculate the displacement I would use</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> s = ut + 1/2 at<sup>2</sup></label></p><p><label class="radio"><input type="radio"> a = (v - u)/t</label></p><p><label class="radio"><input type="radio"> v<sup>2</sup> = u<sup>2</sup> +2as</label></p><p><label class="radio"><input class="c" type="radio"> s = (u + v)t/2</label></p></div><div class="q-explanation"><p>we know u, v and t</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>A car accelerates from rest at 2 ms<sup>-2 </sup> for 10 s</p><p>To calculate the displacement I would use</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> s = (u + v)t/2</label></p><p><label class="radio"><input class="c" type="radio"> s=ut + 1/2at<sup>2</sup></label></p><p><label class="radio"><input type="radio"> v<sup>2</sup> = u<sup>2</sup> +2as</label></p><p><label class="radio"><input type="radio"> a = (v - u)/t</label></p></div><div class="q-explanation"><p>we know u, a and t</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>A car accelerates from rest to 10 ms<sup>-1</sup> covering a distance of 50m</p><p>To calculate the acceleration I would use</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> s = ut + 1/2 at<sup>2</sup></label></p><p><label class="radio"><input type="radio"> a = (v - u)/t</label></p><p><label class="radio"><input class="c" type="radio"> v<sup>2</sup> = u<sup>2</sup> +2as</label></p><p><label class="radio"><input type="radio"> s = (u + v)t/2</label></p></div><div class="q-explanation"><p>we know u, v and s</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">A ball is kicked upwards to a height of 10 m, on the way down it gets stuck 3m up a tree.<p>What is the displacement of the ball?</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> -3 m</label></p><p><label class="radio"><input type="radio"> +8 m</label></p><p><label class="radio"><input class="c" type="radio"> +3 m</label></p><p><label class="radio"><input type="radio"> +5 m</label></p></div><div class="q-explanation"><p>up is +</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>A body has an acceleration of -10 ms<sup>-2</sup> for 10 seconds.</p><p>The final displacement will be negative if the initial velocity is</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 50 ms<sup>-1</sup></label></p><p><label class="radio"><input class="c" type="radio"> 0 ms<sup>-1</sup></label></p><p><label class="radio"><input type="radio"> 100 ms<sup>-1</sup></label></p><p><label class="radio"><input type="radio"> 75 ms<sup>-1</sup></label></p></div><div class="q-explanation"><p>without calculation must be -ve if starting from rest</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">A ball is thrown upwards on the edge of a 50 m high buiding with a velocity of 3 ms<sup>-1</sup>. It goes up then falls to the bottom of the building. To calculate the time taken I would use</div><div class="q-answer"><p><label class="radio"><input type="radio"> a = (v - u)/t</label></p><p><label class="radio"><input type="radio"> v<sup>2</sup> = u<sup>2</sup> +2as</label></p><p><label class="radio"><input class="c" type="radio"> s = ut + 1/2 at<sup>2</sup></label></p><p><label class="radio"><input type="radio"> s = (u + v)t/2</label></p></div><div class="q-explanation"><p>you would have to solve the quadratic but this would be the shortest way</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 diagram represents a problem</p><p style="text-align: center;"><img alt="" height="202" src="../../mc-images/img_0151.jpg" width="395"></p><p>To calculate if the car will hit the pedestrian I would use</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> v<sup>2</sup> = u<sup>2</sup> +2as</label></p><p><label class="radio"><input type="radio"> s = ut + 1/2 at<sup>2</sup></label></p><p><label class="radio"><input type="radio"> a = (v - u)/t</label></p><p><label class="radio"><input type="radio"> s = (u + v)t/2</label></p></div><div class="q-explanation"><p>we don't know u,v and a and want to determine s</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 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<div> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 5</p> </div> </div> <div class="panel-body"> <div> <iframe src="../../../pages/subjects/page-networks/index-17.htm?ticket=082b9c9c4ae3624d&network-id=59&sitename=physics&subject-id=6&fullscreen=false&node=start" style="width: 100%; height: 640px; max-height: 80vh" id="network-59" class="network-viewer"></iframe> </div> </div> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-red"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Just for Fun</p> </div> </div> <div class="panel-body"> <div> <p><em>Which of these suvat equations are true and which are false?</em></p> <p style="text-align: center;"><iframe height="410" src="https://quizlet.com/128702074/spacerace/embed" style="border:0" width="100%"></iframe></p> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="page-container panel-self-assessment" data-id="222"> <div class="panel-heading">MY PROGRESS</div> <div class="panel-body understanding-rate"> <div class="msg"></div> <label class="label-lg">Self-assessment</label><p>How much of <strong>Equations of uniformly accelerated motion</strong> have you understood?</p><div class="slider-container text-center"><div id="self-assessment-slider" class="sib-slider self-assessment " data-value="1" data-percentage=""></div></div> <label class="label-lg">My notes</label> <textarea name="page-notes" class="form-control" rows="3" placeholder="Write your notes here..."></textarea> </div> <div class="panel-footer text-xs-center"> <span id="last-edited" class="mb-xs-3"> </span> <div class="actions mt-xs-3"> <button id="save-my-progress" type="button" class="btn btn-sm btn-primary 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