# Portfolio Type II: Stopping Distances

Anousha Manji

Maths Portfolio Type II- Stopping Distances

The table below shows the average stopping and thinking distances when a person is driving a car and needs to apply the brakes at various speeds.

From this data we can graph two data plots: one showing the relationship between speed versus and the other between speed versus braking distance.

Figure 1

Figure 2

Figure 1 shows a straight line, and therefore it can be said that it is a linear graph. It shows that the correlation between speed and thinking distance is directly proportional and shows the trend that as the speed increases the thinking distance also increases.
The equation of this graph is in the form
, where m is the gradient, and c is the y intercept. The equation can be worked by following these steps:

• Find m (the gradient) using the following equation:

• b is the y intercept but as the graph passes through the origin this value is 0 because while the car is moving at 0 kmh-1 the braking distance is 0 m.
• The final linear equation is  for the domain 32<x<112 because we do not know how long the thinking distance will be for any higher speeds. We could guess from the graph but in a real life situation this would be putting the drivers’ life at risk.

Although finding the equation ...