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PSLE Foundation Mathematics

<p>Two particles, \(A\) and \(B\), leave a point \(O\) at the same time and initially travel in the same direction along the same straight line. Particle \(A\) starts with a velocity \(3 \frac{1}{3} m s^{-1}\) and moves with a constant acceleration of \(4 \frac{1}{3} m s^{-2}\). Particle \(B\) starts with a velocity of \(8 m s^{-1}\) and moves with an acceleration of \(a m s^{-2}\), where&nbsp;\(a = 3 - 2t\) and time \(t\) is the time in seconds after passing point \(O\).</p>
<p>Find</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">the velocity of each particle in terms of \(t\),</div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">the displacement of each particle in terms of \(t\).</div></li></ol>
<p>Hence, find</p>
<ol class="abc-list" start="3"><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph">the distance travelled by Particle \(B\) in the first \(6\) seconds,</div></li><li data-list-item-id="item-d" data-list-item-path="item-d"><div class="list-item-paragraph">the distance from \(O\) at which \(A\) collides with \(B\).</div></li></ol>

Two particles, \(A\) and \(B\), leave a point \(O\) at the same time and initially travel in the same direction along the same straight line. Particle \(A\) starts with a velocity \(3 \frac{1}{3} m s^{-1}\) and moves with a constant acceleration of \(4 \frac{1}{3} m s^{-2}\). Particle \(B\) starts with a velocity of \(8 m s^{-1}\) and moves with an acceleration of \(a m s^{-2}\), where \(a = 3 - 2t\) and time \(t\) is the time in seconds after passing point \(O\).

the velocity of each particle in terms of \(t\),

the displacement of each particle in terms of \(t\).

the distance travelled by Particle \(B\) in the first \(6\) seconds,

the distance from \(O\) at which \(A\) collides with \(B\).

Velocity from Acceleration

Finding the Equation of Displacement from Velocity

Comparing One-Dimensional Motions

Distance Travelled and Average Speed

Kinematics

<p>Two particles, \(A\) and \(B\), leave a point \(O\) at the same time and initially travel in the same direction along the same straight line. Particle \(A\) starts with a velocity of \(4\frac{2}{3}\) m/s and moves with a constant acceleration of \(5\frac{1}{3}\) m/\(\mathrm{s}^2\). Particle \(B\) starts with a velocity of \(10\) m/s and moves with an acceleration of \(a\) m/\(\mathrm{s}^2\), where&nbsp;\(a = 8 - 4t\) and \(t\) is the time in seconds after passing point \(O\).</p>
<p>Find</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">the velocity of each particle in terms of \(t\),</div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">the displacement of each particle in terms of \(t\).</div></li></ol>
<p>Hence, find</p>
<ol class="abc-list" start="3"><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph">the distance travelled by Particle \(B\) in the first \(6\) seconds,</div></li><li data-list-item-id="item-d" data-list-item-path="item-d"><div class="list-item-paragraph">the distance from \(O\) at which \(A\) collides with \(B\).</div></li></ol>

Two particles, \(A\) and \(B\), leave a point \(O\) at the same time and initially travel in the same direction along the same straight line. Particle \(A\) starts with a velocity of \(4\frac{2}{3}\) m/s and moves with a constant acceleration of \(5\frac{1}{3}\) m/\(\mathrm{s}^2\). Particle \(B\) starts with a velocity of \(10\) m/s and moves with an acceleration of \(a\) m/\(\mathrm{s}^2\), where \(a = 8 - 4t\) and \(t\) is the time in seconds after passing point \(O\).

<p>The graph shows the journeys of Gary and Garion between Towns \(P\) and \(Q\) which are \(25\) km apart.</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/converted/1760432173413-0ayp37vn7e3.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvY29udmVydGVkLzE3NjA0MzIxNzM0MTMtMGF5cDM3dm43ZTMucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5Mjc4OTIxNCwiZXhwIjoxNzkyNzg5NTE0fQ.wgKN11Z9VGydhqjkutGTPAfK1zp3IurbCKXQjGAdGcw" style="max-width: min(500px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>Using the graph,</p>
<ol class="abc-list"><li data-list-item-id="item-1760432186813-qrsey6st4" data-list-item-path="item-1760432186813-qrsey6st4"><div class="list-item-paragraph">find the distance Gary was from Town \(Q\) when he stopped for a rest,</div></li><li data-list-item-id="item-1760432187556-writ96inm" data-list-item-path="item-1760432187556-writ96inm"><div class="list-item-paragraph">find the amount of time Gary took to rest,</div></li><li data-list-item-id="item-1760432189821-dss3zzv2y" data-list-item-path="item-1760432189821-dss3zzv2y"><div class="list-item-paragraph">state the time Garion overtook Gary,</div></li><li data-list-item-id="item-1760432190698-tdwfmu264" data-list-item-path="item-1760432190698-tdwfmu264"><div class="list-item-paragraph">find the distance between the two boys at \(1050\),</div></li><li data-list-item-id="item-1760432191853-wygdqshq3" data-list-item-path="item-1760432191853-wygdqshq3"><div class="list-item-paragraph">calculate the average speed for Garion’s whole journey.</div></li></ol>
<p>Editorial clarification: the printed leftmost time label is inconsistent with the uniform scale marked 1100 and 1200. Use that uniform scale throughout; the leftmost origin then corresponds to 1000.</p>

The graph shows the journeys of Gary and Garion between Towns \(P\) and \(Q\) which are \(25\) km apart.

Editorial clarification: the printed leftmost time label is inconsistent with the uniform scale marked 1100 and 1200. Use that uniform scale throughout; the leftmost origin then corresponds to 1000.

Interpreting and Sketching Motion Graphs

Distance–Time Graph of Gary’s and Garion’s Journeys Between Towns P and Q

<p>The diagram below shows the distance-time graph of an object \(A\) from point \(P\) during a one-minute interval.</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/converted/1760432006168-i1lmddo89ik.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvY29udmVydGVkLzE3NjA0MzIwMDYxNjgtaTFsbWRkbzg5aWsucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5Mjc4OTIxNCwiZXhwIjoxNzkyNzg5NTE0fQ.uwwpGajuxNWoT3Tjsk4WNuVWTo91VGYs6xq-I0cKRN8" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li data-list-item-id="item-1760431993575-suavu7cub" data-list-item-path="item-1760431993575-suavu7cub"><div class="list-item-paragraph">Find the average speed of the object during the \(1\) minute interval.</div></li><li data-list-item-id="item-1760431995196-y4cw500b3" data-list-item-path="item-1760431995196-y4cw500b3"><div class="list-item-paragraph">A second object \(B\) travels at a constant speed of \(5\) m/s, starting at point \(P\). On the same axes above, draw the travel graph for this journey. Use your graph to answer the following questions:</div><ol class="i-list"><li data-list-item-id="subitem-1760432019046-18sfwwrj5" data-list-item-path="item-1760431995196-y4cw500b3/subitem-1760432019046-18sfwwrj5"><div class="list-item-paragraph">After how long does object \(A\) meet object \(B\)?</div></li><li data-list-item-id="subitem-1760432019781-1uu63bjm0" data-list-item-path="item-1760431995196-y4cw500b3/subitem-1760432019781-1uu63bjm0"><div class="list-item-paragraph">How long does it take object \(B\) to cover the same total distance as object \(A\)?</div></li></ol></li></ol>

The diagram below shows the distance-time graph of an object \(A\) from point \(P\) during a one-minute interval.

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