A Math

A Math (IGCSE)

E Math

E Math (IGCSE)

H1 Math

H2 Math

IB AA HL Math

IB AA SL Math

IB AI HL Math

IB AI SL Math

IP Math

N(A) A Math

N(A) E Math

PSLE

PSLE Foundation Mathematics

<p>A particle starts from a fixed point \(O\) with velocity \(4\text{ m s}^{-1}\). For the first \(3\) seconds its acceleration is \(2t\text{ m s}^{-2}\). It then begins a second stage of motion; \(T\) seconds after this stage begins, its acceleration is constant at \(-5\text{ m s}^{-2}\).</p>
<ol class="i-list"><li data-list-item-id="amkin-q23-parts-item-1" data-list-item-path="amkin-q23-parts-item-1"><div class="list-item-paragraph">Find the velocity at the end of the first stage and the distance travelled during that stage.<span class="inline-marks">[3]</span></div></li><li data-list-item-id="amkin-q23-parts-item-2" data-list-item-path="amkin-q23-parts-item-2"><div class="list-item-paragraph">Find the time \(T\) at which the particle first comes to rest.<span class="inline-marks">[3]</span></div></li><li data-list-item-id="amkin-q23-parts-item-3" data-list-item-path="amkin-q23-parts-item-3"><div class="list-item-paragraph">Find the total distance travelled from \(O\) before it first comes to rest.<span class="inline-marks">[3]</span></div></li></ol>

A particle starts from a fixed point \(O\) with velocity \(4\text{ m s}^{-1}\). For the first \(3\) seconds its acceleration is \(2t\text{ m s}^{-2}\). It then begins a second stage of motion; \(T\) seconds after this stage begins, its acceleration is constant at \(-5\text{ m s}^{-2}\).

Find the velocity at the end of the first stage and the distance travelled during that stage.

Find the time \(T\) at which the particle first comes to rest.

Find the total distance travelled from \(O\) before it first comes to rest.

Velocity from Acceleration

Piecewise Motion and Changing Time Origins

Distance Travelled and Average Speed

Motion Conditions, Rest and Direction

Two-stage acceleration and braking

Kinematics

<p>A train leaves a station from rest and travels with uniform acceleration. It attains a maximum speed of \(20\) ms\(^{-1}\) after \(4.8\) km. After which it slows down with a uniform acceleration of \(-0.25\) ms\(^{-2}\) to stop at the next station. Find the distance between the stations and the total time of the journey.</p>
<p>Take the direction towards the next station as positive.</p>

A train leaves a station from rest and travels with uniform acceleration. It attains a maximum speed of \(20\) ms\(^{-1}\) after \(4.8\) km. After which it slows down with a uniform acceleration of \(-0.25\) ms\(^{-2}\) to stop at the next station. Find the distance between the stations and the total time of the journey.

Take the direction towards the next station as positive.

Constant-Acceleration Motion

<ol class="abc-list"></ol>
<p>A particle moves in a straight line so that its displacement, \(s\) meters, from a fixed point \(O\) on the straight line is given by \(s=-t^3+3t^2+9t-5\) for \(t \le 4\), where \(t\) is the time in seconds after passing through a point \(P\) on the line.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find</span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">the distance \(OP\),</span></div></li><li><div class="list-item-content"><span class="list-item-text">the distance from \(O\) of the particle when it is instantaneously at rest,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the total distance travelled by the particle during the first \(4\) seconds,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the velocity of the particle when \(t=4\).</span></div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">At \(t=4\) the acceleration of the particle is changed to \((2t-10)\) \(\mathrm{ms}^{-2}\) the instantaneous velocity remaining unchanged and it finally stops at \(Q\) when \(t=T\). Find the value of \(T\).</span></div></li></ol>

A particle moves in a straight line so that its displacement, \(s\) meters, from a fixed point \(O\) on the straight line is given by \(s=-t^3+3t^2+9t-5\) for \(t \le 4\), where \(t\) is the time in seconds after passing through a point \(P\) on the line.

At \(t=4\) the acceleration of the particle is changed to \((2t-10)\) \(\mathrm{ms}^{-2}\) the instantaneous velocity remaining unchanged and it finally stops at \(Q\) when \(t=T\). Find the value of \(T\).

Math Question Bank