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 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

Piecewise Motion and Changing Time Origins

Distance Travelled and Average Speed

Kinematics

<p>A stone is thrown vertically upwards from a bridge over a river with a speed of \(8\) ms\(^{-1}\).</p>
<p>It hits the water with a speed of \(30\) ms\(^{-1}\).</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"><p>the height of the bridge over the water,</p></div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph"><p>the time taken for the stone to hit the water,</p></div></li><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph"><p>the total distance the stone has travelled on its journey.</p></div></li></ol>
<p>Neglect air resistance and use constant gravitational acceleration \(g=9.81\text{ m/s}^2\).</p>

A stone is thrown vertically upwards from a bridge over a river with a speed of \(8\) ms\(^{-1}\).

It hits the water with a speed of \(30\) ms\(^{-1}\).

Neglect air resistance and use constant gravitational acceleration \(g=9.81\text{ m/s}^2\).

<p>A motorcycle passes a police speed check at \(120\) km/h. Seeing a police roadblock ahead, the driver slows down with uniform acceleration to stop after \(100\)m.</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">Find the acceleration of the motorcycle during this period.</div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">Find the time taken to stop.</div></li></ol>
<p>Take the initial direction of motion as positive. During braking, velocity is positive and acceleration is negative, so speed decreases. Negative acceleration alone does not always mean slowing down.</p>

A motorcycle passes a police speed check at \(120\) km/h. Seeing a police roadblock ahead, the driver slows down with uniform acceleration to stop after \(100\)m.

Find the acceleration of the motorcycle during this period.

Take the initial direction of motion as positive. During braking, velocity is positive and acceleration is negative, so speed decreases. Negative acceleration alone does not always mean slowing down.

<p>An MRT train leaves Bishan station from rest and travels along a straight track with uniform acceleration of \(4\) ms\(^{-2}\).</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">What is its velocity \(30\) seconds later?</div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">How far has it travelled in this time?</div></li></ol>

An MRT train leaves Bishan station from rest and travels along a straight track with uniform acceleration of \(4\) ms\(^{-2}\).

What is its velocity \(30\) seconds later?

<p>A ball is dropped from the top of a building. It takes \(7\) seconds to reach the ground.</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">How high is the building?</div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">What is the velocity when it reaches the ground?</div></li></ol>
<p>Hint: We know from Physics that the value of gravitational acceleration \(g\) is \(9.81ms^{-2}\).</p>
<p>Neglect air resistance and use constant gravitational acceleration \(g=9.81\text{ m/s}^2\). The ball is released from rest.</p>

A ball is dropped from the top of a building. It takes \(7\) seconds to reach the ground.

What is the velocity when it reaches the ground?

Hint: We know from Physics that the value of gravitational acceleration \(g\) is \(9.81ms^{-2}\).

Neglect air resistance and use constant gravitational acceleration \(g=9.81\text{ m/s}^2\). The ball is released from rest.

Math Question Bank