Chapter 3: Forces and motion
The chapter problem: the coast road bus
A bus runs along a straight coast road. The driver must be able to stop quickly when a hazard appears.
These are the facts to use all the way through the chapter.
- The bus and its passengers together have a mass of 12000 kg.
- On the open road the bus travels at a steady speed of 12 m/s.
- It accelerates from rest to 12 m/s in 8.0 s.
- When a hazard appears, the driver takes 0.60 s to react before she brakes.
- On a dry road the braking distance from 12 m/s is 9.0 m.
- The hazard is 20 m ahead when the driver first sees it.
- On a wet road the braking distance from 12 m/s is 14 m.
- Later in the chapter, a bus of mass 12000 kg travelling at 12 m/s hits a stationary van of mass 8000 kg, and the two move off together.
By the end of the chapter you will work out the acceleration of the bus and the force that produces it, the distance the bus travels while the driver reacts, its braking force, and its full stopping distance. You will decide whether the bus stops before the hazard on a dry road, and what changes on a wet road. You will also use momentum to work out what happens in the collision.
First contact: no working yet. Estimate. The bus travels at 12 m/s. How far does it move in the 0.60 s before the driver reacts? Is the distance closer to 2 m, 7 m or 12 m? Write your estimate down.
If you are not sure where to start
The bus covers 12 m in every second. The reaction time is a little more than half a second, so the bus moves a little more than half of 12 m. That is close to 7 m.
By the end of this chapter
You will be able to:
- describe the difference between distance and displacement, and between speed and velocity;
- recall some typical speeds, including the speed of sound in air;
- calculate speed, distance and time, and calculate acceleration;
- find speed and acceleration from the gradients of motion graphs;
- use the equation for motion with uniform acceleration;
- describe terminal velocity for an object falling through a fluid;
- state and apply Newton's first, second and third laws of motion;
- calculate force, mass or acceleration using ;
- work out the thinking distance, the braking distance and the stopping distance of a vehicle;
- explain how reaction time, speed and road conditions affect stopping distance;
- explain the dangers of large decelerations.
A few skills are for Higher tier only: reading a speed from the tangent to a curved motion graph, explaining inertia and inertial mass, estimating the force in a large deceleration, and calculating momentum and using conservation of momentum.
Where it is used
Every journey depends on these ideas. So does the design of every car, bus, train and aircraft. Engineers choose the brakes, the tyres and the safety features so that a vehicle can stop in the distance available. The same rules describe a falling stone, a parachute and a rocket.
Your turn to connect it
Where in your own week do you notice speed, or the time something takes to stop? Write two examples. One should be about a journey you make, and one should be about a safety feature you rely on.