A car of mass $1200 \mathrm{kg}$ is driven along a straight horizontal road against a resistance of $5000 \mathrm{N}$. The engine has a maximum power output of $100 \mathrm{kW}$.

Find the maximum speed the car can reach.

A car of mass $1200 \mathrm{kg}$ is driven along a straight horizontal road against a resistance of $5000 \mathrm{N}$. The engine has a maximum power output of $100 \mathrm{kW}$.

Find the power being used when the car is travelling at a speed of $15{ \mathrm{ms}}^{-1}$ and accelerating at $-2{ \mathrm{ms}}^{-2}$.

A box of mass $2 \mathrm{kg}$ is pulled up a rough slope by a rope. The rope passes over a smooth pulley and is attached, at the other end, to a block of mass $4 \mathrm{kg}$ with that end of the rope hanging vertically. The slope is inclined at $20°$ to the horizontal and the coefficient of friction between the slope and the box is $0.3$. The system is released from rest. Use the work energy principle to find the speed of the box when it has moved $1 \mathrm{m}$ up the slope.

A car of mass $1600 \mathrm{kg}$ travels down a straight road inclined at an angle $\theta$ to the horizontal. The power produced by the engine is $24 \mathrm{kW}$ and the non-gravitational resistance is a constant $1600 \mathrm{N}$.

Find the driving force when the car is travelling at a constant $20 \mathrm{m}{ \mathrm{s}}^{-1}$.

A car of mass $1600 \mathrm{kg}$ travels down a straight road inclined at an angle $\theta$ to the horizontal. The power produced by the engine is $24 \mathrm{kW}$ and the non-gravitational resistance is a constant $1600 \mathrm{N}$.

Find the value of $\sin \theta$.

A lorry of mass $14000 \mathrm{kg}$ moves along a road starting from rest at a point $O$. It reaches a point $A$, and then continues to a point $B$ which it reaches with a speed of $24 \mathrm{m}{ \mathrm{s}}^{-1}$. The part $OA$ of the road is straight and horizontal and has length $400 \mathrm{m}$. The part $AB$ of the road is straight and is inclined downwards at an angle of $\theta °$ to the horizontal and has length $300 \mathrm{m}$.

i For the motion from $O$ to $B$, find the gain in kinetic energy of the lorry and express its loss in potential energy in terms of $\theta$. The resistance to the motion of the lorry is $4800 \mathrm{N}$ and the work done by the driving force of the lorry from $O$ to $B$ is $5000 \mathrm{kJ}$.

A lorry of mass $14000 \mathrm{kg}$ moves along a road starting from rest at a point $O$. It reaches a point $A$, and then continues to a point $B$ which it reaches with a speed of $24 \mathrm{m}{ \mathrm{s}}^{-1}$. The part $OA$ of the road is straight and horizontal and has length $400 \mathrm{m}$. The part $AB$ of the road is straight and is inclined downwards at an angle of $\theta °$ to the horizontal and has length $300 \mathrm{m}$.

Find the value of $\theta$.

A block of mass $25 \mathrm{kg}$ is dragged across a rough horizontal floor, using a rope that makes an angle of $30°$ with the floor. The coefficient of friction between the floor and the block is $0.25$. The tension in the rope is $T \mathrm{N}$ and air resistance can be ignored. After travelling a distance of $5 \mathrm{m}$, the speed of the box has increased by $2 \mathrm{m}{ \mathrm{s}}^{-1}$.

Find the work done against friction, in terms of $T$.

A block of mass $25 \mathrm{kg}$ is dragged across a rough horizontal floor, using a rope that makes an angle of $30°$ with the floor. The coefficient of friction between the floor and the block is $0.25$. The tension in the rope is $T \mathrm{N}$ and air resistance can be ignored. After travelling a distance of $5 \mathrm{m}$, the speed of the box has increased by $2 \mathrm{m}{ \mathrm{s}}^{-1}$.

Use the work-energy principle to find, in terms of $T$, the average of the initial and final speeds.