# Stopping Distances

Maths portfolio: Stopping Distances (Standard Level)

Stopping Distances

Before a vehicle stops, the driver has to think before applying the brakes and the brakes take time to actually stop the vehicle. These two processes vary at different speeds as shown the table below:

So by adding the thinking distance and braking distance together we are able to find the total average stopping distance:

Using the records above, our task is to:

• Develop individual functions that model the relationship between speed and thinking distance as well as speed and braking distance
• Develop a model for the relationship between speed and over all stopping distance

1. Using a graphing software I have created two data plots:

Speed versus Thinking distance graph

The values between the thinking distances have a fixed interval and a set value for the speed making it a straight line with a positive constant gradient of 16/3. The gradual increase of the line suggests that as the speed increases the thinking distance increases proportionally.

Since the graph is a linear, the equation y=mx+c can be used to model its behavior where m stands for the gradient and c is the y-intercept.

Using this linear equation, we have to find m:

m=x2- x1
y
2-y1

by substituting theses values to find the gradient from these two co-ordinate points (32,0.006) and (48,0.009):

m=0.009- 0.006 =1.875 x 10^-4
48-32

the y-intercept of the linear is 0 because as the speed is 0 there is no need to think to brake the vehicle so:

c= 0

the final function we get from using the equation ...