6 Robin is driving a car of mass 800 kg along a straight horizontal road at a speed of \(40 \mathrm {~ms} ^ { - 1 }\).
Robin applies the brakes and the car decelerates uniformly; it comes to rest after travelling a distance of 125 m .

1. Show that the resistance force on the car when the brakes are applied is 5120 N .
2. Find the time the car takes to come to rest. For the rest of this question, assume that when Robin applies the brakes there is a constant resistance force of 5120 N on the car. The car returns to its speed of \(40 \mathrm {~ms} ^ { - 1 }\) and the road remains straight and horizontal.
   Robin sees a red light 155 m ahead, takes a short time to react and then applies the brakes.
   The car comes to rest before it reaches the red light.
3. Show that Robin's reaction time is less than 0.75 s . The 'stopping distance' is the total distance travelled while a driver reacts and then applies the brakes to bring the car to rest. For the rest of this question, assume that Robin is still driving the car described above and has a reaction time of 0.675 s . (This is the figure used in calculating the stopping distances given in the Highway Code.)
4. Calculate the stopping distance when Robin is driving at \(20 \mathrm {~ms} ^ { - 1 }\) on a horizontal road. The car then travels down a hill which has a slope of \(5 ^ { \circ }\) to the horizontal.
5. Find the stopping distance when Robin is driving at \(20 \mathrm {~ms} ^ { - 1 }\) down this hill.
6. By what percentage is the stopping distance increased by the fact that the car is going down the hill? Give your answer to the nearest \(1 \%\).