Jan Dangerfield, Stuart Haring and, Julian Gilbey Solutions for Exercise 3: EXERCISE 2B

A learner driver is being tested on the emergency stop. The car has mass $1250 \mathrm{kg}$ and is moving at $21 \mathrm{m}{ \mathrm{s}}^{-1}.$ When the driver presses the brakes there is a braking force of $10000 \mathrm{N}$ in addition to the air resistance of $500 \mathrm{N}.$ Find the distance covered in coming to rest.

A small aircraft is accelerating on a runway. Its engines provide a constant driving force of $20 \mathrm{kN}.$ There is average air resistance of $1000 \mathrm{N}.$ The aircraft starts from rest and leaves the runway, which is $900 \mathrm{m}$ long, with speed $80 \mathrm{m}{ \mathrm{s}}^{-1}.$ Find the mass of the aircraft.

A small aircraft is accelerating on a runway. Its engines provide a constant driving force of $20 \mathrm{kN}.$ There is average air resistance of $1000 \mathrm{N}.$The aircraft starts from rest and leaves the runway, which is $900 \mathrm{m}$ long, with speed $80 \mathrm{m}{ \mathrm{s}}^{-1}.$What assumptions have been made to answer the question?

A drag racing car races on a track of length $400 \mathrm{m}.$ The car has mass $600 \mathrm{kg}$ and accelerates from rest with a constant driving force of $21 \mathrm{kN}.$ There is air resistance of $1800 \mathrm{N}.$ Find the speed of the car at the finish line of the race.

A wooden block of mass $6 \mathrm{kg}$ is being dragged along a horizontal surface by a force of $10 \mathrm{N}.$ It accelerates from $1{ \mathrm{ms}}^{-1}$ to $3{ \mathrm{ms}}^{-1}$ in $4 \mathrm{s}.$ Find the size of the friction force acting on the wooden block.

A motorcyclist is travelling at $20 \mathrm{m}{ \mathrm{s}}^{-1}$ on level road when she approaches roadworks and slows down to $10{ \mathrm{ms}}^{-1}$ over a distance of $250 \mathrm{m}.$The combined mass of the motorcyclist and the motorcycle is $360 \mathrm{kg}.$ There is air resistance of $80 \mathrm{N}.$ Find the braking force of the motorcycle.

An aeroplane of mass $8$ tonnes is flying horizontally through the air at $240 \mathrm{m}{ \mathrm{s}}^{-1}$. There is air resistance of $20 \mathrm{kN}.$ The pilot reduces the driving force from the engines to slow to $160 \mathrm{m}{ \mathrm{s}}^{-1}$ over $40 \mathrm{s}$ before starting to descend. Find the magnitude of the reduced driving force.

A car of mass $1400 \mathrm{kg}$ slows down from $30 \mathrm{m}{ \mathrm{s}}^{-1}$ to $20 \mathrm{m}{ \mathrm{s}}^{-1}$ when the driver sees a sign for reduced speed limit $400 \mathrm{m}$ ahead. There is air resistance of $1000 \mathrm{N}.$ Determine whether the driver needs to provide a braking force or just reduce the amount of driving force exerted, and find the size of the force.