GCE Advanced Level (Sri Lanka) · Combined Mathematics

Applied Maths: Kinematics, Dynamics, Energy and Momentum

62 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 62 questions

A particle is projected from level ground with speed $100 m s^{- 1}$ at an angle $α$ to the horizontal, $sin α = \frac{3}{5}$ . Find the time of flight. (Take $g = 10 m s^{- 2}$ .)
Two particles of masses $6 kg$ and $4 kg$ are connected by a light inextensible string over a smooth fixed pulley. Find the acceleration. (Take $g = 10 m s^{- 2}$ .)
A particle of mass $4 kg$ lies on a smooth horizontal table, joined by a light string over a smooth pulley at the edge to a particle of mass $3 kg$ hanging vertically. Find the accelerat…
Particles of masses $4$ , $4$ and $3 kg$ are placed on a line at $x = 0$ , $2$ and $5 m$ . Find the $x$ -coordinate of their centre of mass.
A particle of mass $4 kg$ moves in a horizontal circle of radius $4 m$ at a constant speed of $3 m s^{- 1}$ on the end of a light string. Find the tension.
A particle is projected from level ground with speed $100 m s^{- 1}$ at an angle $α$ where $sin α = \frac{3}{5}$ . Find the greatest height reached. (Take $g = 10 m s^{- 2}$ .)
Two particles of masses $5 kg$ and $3 kg$ are connected by a light inextensible string over a smooth fixed pulley. Find the tension in the string. (Take $g = 10 m s^{- 2}$ .)
A particle of mass $10 kg$ falls freely from rest through a height of $20 m$ . Find its speed on reaching the ground. (Take $g = 10 m s^{- 2}$ .)
Particles of masses $3$ , $4$ and $4 kg$ are placed on a line at $x = 2$ , $3$ and $8 m$ . Find the $x$ -coordinate of their centre of mass.
A particle of mass $1 kg$ moves in a horizontal circle of radius $8 m$ at a constant speed of $5 m s^{- 1}$ on the end of a light string. Find the tension.
Two particles of masses $9 kg$ and $1 kg$ are connected by a light inextensible string over a smooth fixed pulley. Find the acceleration. (Take $g = 10 m s^{- 2}$ .)
A particle of mass $6 kg$ lies on a smooth horizontal table, joined by a light string over a smooth pulley at the edge to a particle of mass $3 kg$ hanging vertically. Find the accelerat…
Find the kinetic energy of a particle of mass $10 kg$ moving at $5 m s^{- 1}$ .
Particles of masses $3$ , $1$ and $4 kg$ are placed on a line at $x = 4$ , $6$ and $8 m$ . Find the $x$ -coordinate of their centre of mass.
A particle of mass $1 kg$ moves in a horizontal circle of radius $2 m$ at a constant speed of $4 m s^{- 1}$ on the end of a light string. Find the tension.
A particle is projected from level ground with speed $25 m s^{- 1}$ at an angle $α$ where $sin α = \frac{3}{5}$ . Find the greatest height reached. (Take $g = 10 m s^{- 2}$ .)
Two particles of masses $3 kg$ and $2 kg$ are connected by a light inextensible string over a smooth fixed pulley. Find the tension in the string. (Take $g = 10 m s^{- 2}$ .)
A particle of mass $4 kg$ lies on a smooth horizontal table, joined by a light string over a smooth pulley at the edge to a particle of mass $2 kg$ hanging vertically. Find the accelerat…
A particle of mass $2 kg$ falls freely from rest through a height of $45 m$ . Find its speed on reaching the ground. (Take $g = 10 m s^{- 2}$ .)
Particles of masses $2$ , $2$ and $1 kg$ are placed on a line at $x = 0$ , $6$ and $9 m$ . Find the $x$ -coordinate of their centre of mass.
A particle of mass $1 kg$ moves in a horizontal circle of radius $6 m$ at a constant speed of $4 m s^{- 1}$ on the end of a light string. Find the tension.
Two particles of masses $4 kg$ and $1 kg$ are connected by a light inextensible string over a smooth fixed pulley. Find the acceleration. (Take $g = 10 m s^{- 2}$ .)
A particle of mass $6 kg$ lies on a smooth horizontal table, joined by a light string over a smooth pulley at the edge to a particle of mass $4 kg$ hanging vertically. Find the accelerat…
Particles of masses $5$ , $2$ and $2 kg$ are placed on a line at $x = 1$ , $2$ and $5 m$ . Find the $x$ -coordinate of their centre of mass.
A particle of mass $1 kg$ moves in a horizontal circle of radius $2 m$ at a constant speed of $6 m s^{- 1}$ on the end of a light string. Find the tension.
A ball is projected from level ground with speed $100 m s^{- 1}$ at an angle $α$ with $sin α = \frac{3}{5}$ . Find the horizontal range. (Take $g = 10 m s^{- 2}$ .)
A particle of mass $2 kg$ lies on a smooth horizontal table, joined by a light string over a smooth pulley at the edge to a particle of mass $1 kg$ hanging vertically. Find the accelerat…
A car moves at a constant speed of $25 m s^{- 1}$ while its engine works at $4000 W$ . Find the driving force.
Particles of masses $5$ , $1$ and $1 kg$ are placed on a line at $x = 5$ , $7$ and $9 m$ . Find the $x$ -coordinate of their centre of mass.
A particle of mass $2 kg$ moves in a horizontal circle of radius $8 m$ at a constant speed of $5 m s^{- 1}$ on the end of a light string. Find the tension.
Two particles of masses $7 kg$ and $3 kg$ are connected by a light inextensible string over a smooth fixed pulley. Find the acceleration. (Take $g = 10 m s^{- 2}$ .)
A force of $30 N$ acts at an angle $θ$ to the horizontal, where $cos θ = \frac{4}{5}$ , and moves a body $8 m$ along a horizontal floor. Find the work done by the force.
Particles of masses $1$ , $5$ and $5 kg$ are placed on a line at $x = 1$ , $5$ and $6 m$ . Find the $x$ -coordinate of their centre of mass.
A particle of mass $4 kg$ moves in a horizontal circle of radius $6 m$ at a constant speed of $6 m s^{- 1}$ on the end of a light string. Find the tension.
A particle is projected from level ground with speed $50 m s^{- 1}$ at an angle $α$ where $sin α = \frac{3}{5}$ . Find the greatest height reached. (Take $g = 10 m s^{- 2}$ .)
A particle of mass $2 kg$ lies on a smooth horizontal table, joined by a light string over a smooth pulley at the edge to a particle of mass $4 kg$ hanging vertically. Find the accelerat…
A force of $30 N$ acts at an angle $θ$ to the horizontal, where $cos θ = \frac{4}{5}$ , and moves a body $5 m$ along a horizontal floor. Find the work done by the force.
Particles of masses $5$ , $5$ and $1 kg$ are placed on a line at $x = 2$ , $4$ and $8 m$ . Find the $x$ -coordinate of their centre of mass.
A particle of mass $2 kg$ moves in a horizontal circle of radius $4 m$ at a constant speed of $5 m s^{- 1}$ on the end of a light string. Find the tension.
A ball is projected from level ground with speed $50 m s^{- 1}$ at an angle $α$ with $sin α = \frac{3}{5}$ . Find the horizontal range. (Take $g = 10 m s^{- 2}$ .)
Two particles of masses $9 kg$ and $1 kg$ are connected by a light inextensible string over a smooth fixed pulley. Find the tension in the string. (Take $g = 10 m s^{- 2}$ .)
A particle of mass $6 kg$ lies on a smooth horizontal table, joined by a light string over a smooth pulley at the edge to a particle of mass $1 kg$ hanging vertically. Find the accelerat…
A particle of mass $2 kg$ falls freely from rest through a height of $20 m$ . Find its speed on reaching the ground. (Take $g = 10 m s^{- 2}$ .)
Particles of masses $3$ , $4$ and $5 kg$ are placed on a line at $x = 3$ , $8$ and $9 m$ . Find the $x$ -coordinate of their centre of mass.
A particle of mass $2 kg$ moves in a horizontal circle of radius $2 m$ at a constant speed of $4 m s^{- 1}$ on the end of a light string. Find the tension.
A particle starts with speed $5 m s^{- 1}$ and accelerates uniformly at $3 m s^{- 2}$ . Find its speed after $5 s$ .
A particle is projected from level ground with speed $50 m s^{- 1}$ at an angle $α$ to the horizontal, $sin α = \frac{3}{5}$ . Find the time of flight. (Take $g = 10 m s^{- 2}$ .)
Two particles of masses $7 kg$ and $3 kg$ are connected by a light inextensible string over a smooth fixed pulley. Find the tension in the string. (Take $g = 10 m s^{- 2}$ .)
A car moves at a constant speed of $25 m s^{- 1}$ while its engine works at $3000 W$ . Find the driving force.
Particles of masses $4$ , $3$ and $3 kg$ are placed on a line at $x = 2$ , $3$ and $6 m$ . Find the $x$ -coordinate of their centre of mass.
A particle of mass $1 kg$ moves in a horizontal circle of radius $2 m$ at a constant speed of $5 m s^{- 1}$ on the end of a light string. Find the tension.
A particle starts with speed $12 m s^{- 1}$ and accelerates uniformly at $2 m s^{- 2}$ . Find its speed after $4 s$ .
Two particles of masses $3 kg$ and $2 kg$ are connected by a light inextensible string over a smooth fixed pulley. Find the acceleration. (Take $g = 10 m s^{- 2}$ .)
A particle of mass $4 kg$ lies on a smooth horizontal table, joined by a light string over a smooth pulley at the edge to a particle of mass $1 kg$ hanging vertically. Find the accelerat…
A particle of mass $5 kg$ moving at $6 m s^{- 1}$ collides with a particle of mass $1 kg$ at rest. They coalesce. Find their common speed.
Particles of masses $1$ , $1$ and $5 kg$ are placed on a line at $x = 2$ , $3$ and $9 m$ . Find the $x$ -coordinate of their centre of mass.
A particle starts with speed $4 m s^{- 1}$ and accelerates uniformly at $1 m s^{- 2}$ . Find its speed after $4 s$ .
A particle of mass $3 kg$ lies on a smooth horizontal table, joined by a light string over a smooth pulley at the edge to a particle of mass $2 kg$ hanging vertically. Find the accelerat…
Find the kinetic energy of a particle of mass $2 kg$ moving at $10 m s^{- 1}$ .
Particles of masses $5$ , $2$ and $1 kg$ are placed on a line at $x = 0$ , $1$ and $9 m$ . Find the $x$ -coordinate of their centre of mass.
A particle of mass $1 kg$ moves in a horizontal circle of radius $4 m$ at a constant speed of $3 m s^{- 1}$ on the end of a light string. Find the tension.
Two particles of masses $6 kg$ and $4 kg$ are connected by a light inextensible string over a smooth fixed pulley. Find the tension in the string. (Take $g = 10 m s^{- 2}$ .)

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