A car of mass $1800 \mathrm{kg}$ is being driven, at a constant $15 \mathrm{m}{ \mathrm{s}}^{-1}$, against a resistance of $2000 \mathrm{N}$, up a hill inclined at $10°$ to the horizontal. Find the rate at which the engine is working.

A small van of mass $1600 \mathrm{kg}$accelerates from rest in a straight line along a horizontal road. The resistance from friction and air resistance is $2400 \mathrm{N}$ throughout the motion. The engine works at a constant rate of $48 \mathrm{kW}$.

Write down an expression for the driving force when the van is travelling at $v \mathrm{m}{ \mathrm{s}}^{-1}$.

A small van of mass $1600 \mathrm{kg}$accelerates from rest in a straight line along a horizontal road. The resistance from friction and air resistance is $2400 \mathrm{N}$ throughout the motion. The engine works at a constant rate of $48 \mathrm{kW}$.

Write down an expression for the acceleration of the van when it is travelling at $v{ \mathrm{ms}}^{-1}$.

A small van of mass $1600 \mathrm{kg}$accelerates from rest in a straight line along a horizontal road. The resistance from friction and air resistance is $2400 \mathrm{N}$ throughout the motion. The engine works at a constant rate of $48 \mathrm{kW}$.

Explain why the power cannot be constant.

A powerboat of mass $500 \mathrm{kg}$ travels in a straight line at its maximum velocity against a resistance of $15 \mathrm{N}$. The engine of the powerboat has a maximum power output of $750 \mathrm{W}$.

Find the maximum velocity.

A powerboat of mass $500 \mathrm{kg}$ travels in a straight line at its maximum velocity against a resistance of $15 \mathrm{N}$. The engine of the powerboat has a maximum power output of $750 \mathrm{W}$.

In different weather conditions the same powerboat has a maximum velocity of only 25 $m{s}^{-1}$

State what has changed in the model and give the new value of this quantity.