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PSLE Foundation Mathematics

<p>A particle travels in a straight line so that its velocity, \(v\) m/s, is given by \(v = -2t^2 + 6t + 4\), where&nbsp;\(t\) seconds is the time after passing \(O\). Find an expression in terms of \(t\) for</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph"><p>its acceleration,</p></div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph"><p>its displacement from \(O\),</p></div></li><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph"><p>the values of \(t\) when the speed is \(3\) m/s,</p></div></li><li data-list-item-id="item-d" data-list-item-path="item-d"><div class="list-item-paragraph"><p>the values of \(t\) when the displacement of the particle is \(0\) m.</p></div></li></ol>

A particle travels in a straight line so that its velocity, \(v\) m/s, is given by \(v = -2t^2 + 6t + 4\), where \(t\) seconds is the time after passing \(O\). Find an expression in terms of \(t\) for

Finding the Equation of Displacement from Velocity

Differentiating Displacement and Velocity

Motion Conditions, Rest and Direction

Kinematics

<p>A particle moves in a straight line with a velocity, \(v\) m s\(^{-1}\). Its velocity can be modelled by the equation \(v = \sin t + t \cos t\). Given the initial conditions \(t = 0\), \(s = 0\).</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">Differentiate \(s = t \sin t\) with respect to \(t\).</div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">Hence find an expression for the displacement, \(s\) at time \(t\)</div></li><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph">Find an expression for the acceleration, \(a\), at time \(t\).</div></li><li data-list-item-id="item-d" data-list-item-path="item-d"><div class="list-item-paragraph">Determine whether the motion is periodic, and justify your answer.</div></li><li data-list-item-id="item-e" data-list-item-path="item-e"><div class="list-item-paragraph">What happens to the amplitude of the motion as time progresses?</div></li></ol>

A particle moves in a straight line with a velocity, \(v\) m s\(^{-1}\). Its velocity can be modelled by the equation \(v = \sin t + t \cos t\). Given the initial conditions \(t = 0\), \(s = 0\).

Differentiate \(s = t \sin t\) with respect to \(t\).

Hence find an expression for the displacement, \(s\) at time \(t\)

Find an expression for the acceleration, \(a\), at time \(t\).

Determine whether the motion is periodic, and justify your answer.

What happens to the amplitude of the motion as time progresses?

Integration as an Inverse Process of Differentiation

Interpreting Motion Models

Product Rule

Integration

Differentiation

<p>A particle travels in a straight line such that, \(t\) s after passing a fixed point, \(O\), its velocity is given by \(v = 8 \cos \left( \frac{t}{2} \right).\) 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 value of \(t\) when&nbsp;\(v = 4\) for the first time</div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">The acceleration when&nbsp;\(t = 2\)</div></li><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph">The distance from \(O\) when&nbsp;\(v = 0\) for the first time.</div></li></ol>

A particle travels in a straight line such that, \(t\) s after passing a fixed point, \(O\), its velocity is given by \(v = 8 \cos \left( \frac{t}{2} \right).\) Find:

The value of \(t\) when \(v = 4\) for the first time

The distance from \(O\) when \(v = 0\) for the first time.

<p>A particle moving in a straight line passes a fixed point \(O\) on the line with its velocity \(36 \text{ ms}^{-1}\). The acceleration, \(a \text{ ms}^{-2}\), of the particle, \(t\) seconds after passing \(O\), is given by \(a = 5 - 2t\). Calculate</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 the particle \(4\) seconds after passing \(O\)</div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">The time taken to reach the maximum distance from \(O\) in the direction of the initial motion</div></li><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph">This maximum distance</div></li></ol>

A particle moving in a straight line passes a fixed point \(O\) on the line with its velocity \(36 \text{ ms}^{-1}\). The acceleration, \(a \text{ ms}^{-2}\), of the particle, \(t\) seconds after passing \(O\), is given by \(a = 5 - 2t\). Calculate

The velocity of the particle \(4\) seconds after passing \(O\)

The time taken to reach the maximum distance from \(O\) in the direction of the initial motion

Velocity from Acceleration

Maximum and Minimum Motion Quantities

<p>A particle starts from rest at \(O\) and moves in a straight line with its acceleration, \(a\,ms^{-2}\), given by the equation \(a = 6 - 3t\), where&nbsp;\(t\) seconds is the time after leaving a fixed point \(O\). The particle comes to instantaneous rest at a point \(A\). 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 time taken for the particle to reach \(A\),</div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">The distance \(OA\)</div></li><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph">The maximum speed of the particle during its motion from \(O\) to \(A\).</div></li></ol>

A particle starts from rest at \(O\) and moves in a straight line with its acceleration, \(a\,ms^{-2}\), given by the equation \(a = 6 - 3t\), where \(t\) seconds is the time after leaving a fixed point \(O\). The particle comes to instantaneous rest at a point \(A\). Find

the time taken for the particle to reach \(A\),

The maximum speed of the particle during its motion from \(O\) to \(A\).

<p>A particle passes a fixed point \(O\) with a velocity of \(5\) m/s and moves in a straight line with an acceleration of \(a = 2(5 - t)\) \(ms^{-2}\), where&nbsp;\(t\) seconds is the time after passing \(O\). Calculate</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">the value of \(t\) when the velocity is again \(5\) m/s</div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">the displacement of the particle at this instant.</div></li></ol>

A particle passes a fixed point \(O\) with a velocity of \(5\) m/s and moves in a straight line with an acceleration of \(a = 2(5 - t)\) \(ms^{-2}\), where \(t\) seconds is the time after passing \(O\). Calculate

the value of \(t\) when the velocity is again \(5\) m/s

the displacement of the particle at this instant.

<p>A particle moves in a straight line. Its velocity \(v\) m/s at time \(t\) seconds is given by \(v = t^2 - 5t - 6\), The displacement \(s\) metres, at time \(t\) seconds is measured from a fixed origin \(O\).</p>
<p>When&nbsp;\(t = 0\), its displacement, \(s=5\) metres, 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 value of \(t\) when the particle is at rest and the displacement at this instant,</div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">the displacement when&nbsp;\(t = 2\) and the total distance travelled by the particle in the first \(2\) seconds</div></li></ol>

A particle moves in a straight line. Its velocity \(v\) m/s at time \(t\) seconds is given by \(v = t^2 - 5t - 6\), The displacement \(s\) metres, at time \(t\) seconds is measured from a fixed origin \(O\).

When \(t = 0\), its displacement, \(s=5\) metres, find

the value of \(t\) when the particle is at rest and the displacement at this instant,

the displacement when \(t = 2\) and the total distance travelled by the particle in the first \(2\) seconds

Distance Travelled and Average Speed

<p>A particle moves in a straight line from a point \(O\), such that&nbsp;\(t\) seconds after leaving \(O\), its velocity, \(v\) m/s is given by \(v = e^{0.2t} + 4\).</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">Calculate the initial acceleration of the particle.</div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">Calculate the displacement of the particle when&nbsp;\(t = 2\) s</div></li><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph">Will the particle return to \(O\)?</div></li></ol>

A particle moves in a straight line from a point \(O\), such that \(t\) seconds after leaving \(O\), its velocity, \(v\) m/s is given by \(v = e^{0.2t} + 4\).

Calculate the initial acceleration of the particle.

Calculate the displacement of the particle when \(t = 2\) s

<p>A particle travelling in a straight line starts from rest at point \(O\) and has acceleration (in \(\text{m s}^{-2}\)) <br>Modelled by the equation \(a = 12 - 8t\), where&nbsp;\(t\) is measured in seconds.</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">Find an expression for the velocity of the particle at time \(t\).</div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">Find an expression for the position of the particle at time \(t\).</div></li><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph">Find its furthest distance from \(O\) in a positive direction during the subsequent motion.</div></li><li data-list-item-id="item-d" data-list-item-path="item-d"><div class="list-item-paragraph">Find the time taken for the particle to return to \(O\), and its velocity at that time.</div></li><li data-list-item-id="item-e" data-list-item-path="item-e"><div class="list-item-paragraph">Describe the motion of the particle after it passes through \(O\) for the second time.</div></li></ol>

A particle travelling in a straight line starts from rest at point \(O\) and has acceleration (in \(\text{m s}^{-2}\)) 
Modelled by the equation \(a = 12 - 8t\), where \(t\) is measured in seconds.

Find an expression for the velocity of the particle at time \(t\).

Find an expression for the position of the particle at time \(t\).

Find its furthest distance from \(O\) in a positive direction during the subsequent motion.

Find the time taken for the particle to return to \(O\), and its velocity at that time.

Describe the motion of the particle after it passes through \(O\) for the second time.

Speeding Up and Slowing Down

<p>A particle passes a fixed point \(O\) with a velocity of \(6\) \(ms^{-1}\) and moves in a straight line with an acceleration of \(3(4 - t)\) \(ms^{-2}\), where&nbsp;\(t\) seconds is the time after passing \(O\). Calculate</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">The value of \(t\) when the velocity is again \(6\) \(ms^{-1}\)</div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">The position of the particle at this instant</div></li></ol>

A particle passes a fixed point \(O\) with a velocity of \(6\) \(ms^{-1}\) and moves in a straight line with an acceleration of \(3(4 - t)\) \(ms^{-2}\), where \(t\) seconds is the time after passing \(O\). Calculate

The value of \(t\) when the velocity is again \(6\) \(ms^{-1}\)

The position of the particle at this instant

<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 \(B\).

Comparing One-Dimensional Motions

<p>The velocity of a particle, in \(ms^{-1}\), moving in a straight line, \(t\) \(s\) after passing a fixed point, \(O\), is given by the equation \(v = 12t - 2t^{2}\). 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 time at which the velocity reaches a maximum.</div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">The positive time at which the particle next comes instantaneously to rest.</div></li><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph">The distance from \(O\) at that positive rest time.</div></li><li data-list-item-id="item-d" data-list-item-path="item-d"><div class="list-item-paragraph">The speed of the particle when it passes \(O\) again.</div></li></ol>

The velocity of a particle, in \(ms^{-1}\), moving in a straight line, \(t\) \(s\) after passing a fixed point, \(O\), is given by the equation \(v = 12t - 2t^{2}\). Find:

The time at which the velocity reaches a maximum.

The positive time at which the particle next comes instantaneously to rest.

The distance from \(O\) at that positive rest time.

The speed of the particle when it passes \(O\) again.

<p>A particle moves in a straight line such that at time \(t\) seconds after leaving a fixed point \(O\), its velocity \(v\) m/s is given by \(v = 6e^{-\frac{1}{4}t}\). Find</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">An expression for the displacement of the particle from \(O\)</div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">The displacement at \(t = 6\)</div></li></ol>

A particle moves in a straight line such that at time \(t\) seconds after leaving a fixed point \(O\), its velocity \(v\) m/s is given by \(v = 6e^{-\frac{1}{4}t}\). Find

An expression for the displacement of the particle from \(O\)

<p>A particle \(P\) leaves a fixed point \(O\) and moves in a straight line so that, \(t\) s after leaving point \(O\), its velocity \(v\) m/s, is given by \(v = 3\sin 2t + 2\).</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find, when \(t = 10\),</span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">the velocity of \(P\),</span></div></li><li><div class="list-item-content"><span class="list-item-text">the displacement of \(P\) from \(O\).</span></div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">Calculate</span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">the value of \(t\) when \(P\) comes to instantaneous rest for the second time,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the total distance it has travelled when \(t = \frac{3}{4}\pi\).</span></div></li></ol></li></ol>

A particle \(P\) leaves a fixed point \(O\) and moves in a straight line so that, \(t\) s after leaving point \(O\), its velocity \(v\) m/s, is given by \(v = 3\sin 2t + 2\).

<p>A particle \(P\) moves along a straight line such that&nbsp;\(t\) seconds after passing through a fixed point \(O\), its velocity is given by \(v = \frac{1}{2}e^{2t} - 4\). The particle comes to instantaneous rest at a point \(A\).</p>
<ol class="abc-list"><li data-list-item-id="item-q5-a" data-list-item-path="item-q5-a"><div class="list-item-paragraph">Find an expression, in terms of \(t\), for the acceleration of \(P\).</div></li><li data-list-item-id="item-q5-b" data-list-item-path="item-q5-b"><div class="list-item-paragraph">Find an expression, in terms of \(t\), for the displacement of \(P\).</div></li><li data-list-item-id="item-q5-c" data-list-item-path="item-q5-c"><div class="list-item-paragraph">Show that the time taken for&nbsp;\(P\) to travel from \(O\) to \(A\) is \(\frac{1}{2}\ln 8\) seconds.</div></li><li data-list-item-id="item-q5-d" data-list-item-path="item-q5-d"><div class="list-item-paragraph">Given that&nbsp;\(P\) passes through a point \(B\) when&nbsp;\(t = 3\), find the average speed of \(P\) from \(A\) to \(B\).</div></li></ol>

A particle \(P\) moves along a straight line such that \(t\) seconds after passing through a fixed point \(O\), its velocity is given by \(v = \frac{1}{2}e^{2t} - 4\). The particle comes to instantaneous rest at a point \(A\).

Find an expression, in terms of \(t\), for the acceleration of \(P\).

Find an expression, in terms of \(t\), for the displacement of \(P\).

Show that the time taken for \(P\) to travel from \(O\) to \(A\) is \(\frac{1}{2}\ln 8\) seconds.

Given that \(P\) passes through a point \(B\) when \(t = 3\), find the average speed of \(P\) from \(A\) to \(B\).

<p>A particle moves in a straight line so that, at time \(t\) seconds after leaving a fixed point \(O\), its velocity, \(v\) ms\({}^{-1}\), is given by \(v = 7 - 6e^{1-\frac{1}{2}t}\). Find</p>
<ol class="abc-list"><li data-list-item-id="item-q4-a" data-list-item-path="item-q4-a"><div class="list-item-paragraph">the initial acceleration of the particle,</div></li><li data-list-item-id="item-q4-b" data-list-item-path="item-q4-b"><div class="list-item-paragraph">the value of \(t\) when the particle is instantaneously at rest,</div></li><li data-list-item-id="item-q4-c" data-list-item-path="item-q4-c"><div class="list-item-paragraph">the distance of the particle from \(O\) when&nbsp;\(t = 2\).</div></li></ol>

A particle moves in a straight line so that, at time \(t\) seconds after leaving a fixed point \(O\), its velocity, \(v\) ms\({}^{-1}\), is given by \(v = 7 - 6e^{1-\frac{1}{2}t}\). Find

the initial acceleration of the particle,

the value of \(t\) when the particle is instantaneously at rest,

the distance of the particle from \(O\) when \(t = 2\).

<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 \(O\).

<ol class="abc-list"></ol>
<p>A particle moves in a straight line so that, \(t\) seconds after passing through a fixed point \(O\), its velocity \(v\) ms\({}^{-1}\), is given by \(v=3e^t-40e^{-2t}\). Find</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the initial velocity of the particle.</span></div></li><li><div class="list-item-content"><span class="list-item-text">the value of \(t\) when the particle is instantaneously at rest.</span></div></li><li><div class="list-item-content"><span class="list-item-text">the acceleration of the particle when&nbsp;\(t=\ln 2\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">the value of \(t\) when the acceleration is minimum.</span></div></li><li><div class="list-item-content"><span class="list-item-text">an expression for the displacement in terms of \(t\).</span></div></li></ol>

A particle moves in a straight line so that, \(t\) seconds after passing through a fixed point \(O\), its velocity \(v\) ms\({}^{-1}\), is given by \(v=3e^t-40e^{-2t}\). Find

the value of \(t\) when the particle is instantaneously at rest.

the acceleration of the particle when \(t=\ln 2\).

the value of \(t\) when the acceleration is minimum.

an expression for the displacement in terms of \(t\).

<p>An object at \(A\), with an initial displacement of \(3\) m to the right from a fixed point \(O\), travels in a straight line so that its velocity, \(v\) ms\({}^{-1}\), is given by \(v = t^2 - 5t + 6\) where \(t\) is the time in seconds after leaving \(A\).</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find the values of \(t\) when the object comes to an instantaneous rest.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the acceleration of the object at \(t = 5\) s.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Obtain an expression, in terms of \(t\), for the displacement of the object from \(O\) after \(t\) seconds.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the average speed of the object in the first \(5\) seconds.</span></div></li></ol>

An object at \(A\), with an initial displacement of \(3\) m to the right from a fixed point \(O\), travels in a straight line so that its velocity, \(v\) ms\({}^{-1}\), is given by \(v = t^2 - 5t + 6\) where \(t\) is the time in seconds after leaving \(A\).

Find the values of \(t\) when the object comes to an instantaneous rest.

Find the acceleration of the object at \(t = 5\) s.

Obtain an expression, in terms of \(t\), for the displacement of the object from \(O\) after \(t\) seconds.

Find the average speed of the object in the first \(5\) seconds.

<p>A particle \(P\) moves in a straight line such that&nbsp;\(t\) seconds after starting at displacement \(-3\) metres from \(O\), its velocity, \(v\) m/s, is given by \(v = 3t^2 + 13t - 10\). Find</p>
<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-paragraph">\(t\) when the particle changes direction.</div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">an expression for the displacement of the particle from \(O\).</div></li></ol>

A particle \(P\) moves in a straight line such that \(t\) seconds after starting at displacement \(-3\) metres from \(O\), its velocity, \(v\) m/s, is given by \(v = 3t^2 + 13t - 10\). Find

\(t\) when the particle changes direction.

an expression for the displacement of the particle from \(O\).

Math Question Bank