# An Analysis of Braking Distance and its Relationship with Speed and Distance Travelled

Topics: Quadratic equation, Elementary algebra, Linear equation Pages: 4 (808 words) Published: June 8, 2013
Breaking distances:
Introduction:
Drivers must pay attention to their surroundings. This includes calculating the braking distance from the cars and objects around a driver. With this the driver can avoid accidents and can save lives and money. As shown in the picture above. The prime factors that apply that have a big impact on the actual stopping distances in the real world: Weather, road conditions, type and condition of vehicle, load etc , not to mention the age, health and mental ability of the driver. These all can affect the time taken to react and stop the vehicle. In this investigation we will find distance the car traveled after the breaks were applied. There are emergency cases when the car needs to stop . However when the car breaks are applied, it will still move a certain distance known as the” breaking distance”.

The table below shows the breaking distances that were obtained at different speeds:

If we show the relationship of the speed and the breaking distance by plotting a graph like this one: If we want to get an equation that helps us identify the relationship between the Speed and the breaking distance. We can see that the line makes a form of a parabola so we drive it through out calculator to get the following results: We believe that the data is Quadratic because it goes in a parabola: Thus; When: y=ax2 +bx+c

a=0.004
b=0.203
c=-6.428
Thus we come up with this equation:
Y= (0.004x X2) + 0.203xX -6.428
To make the equation more realistic we can change the X and Y variables into: The X variable into “V” for Speed
The Y variable into “S” for Breaking distance
S= (0.004x V2) + 0.203VS -6.428
If we drive this through the calculator and plot the graph we obtain this parabola

However we can find other equations that can be derived with these values to obtain similar results: Linear equations:

Here our:
Breaking distance is S
Speed is V
So when:
S=aV+b
We plot the above values in the GDC and got the...