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stopping distance

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Introduction

5 Stopping distances

Method

1. Through the use Chart Wizard on Microsoft Excel, I have generated the following graphs:

image01.png

image02.png

Already, we see that thinking distance is a linear function. From 32km/hr onwards, every time speed increases by 16km/hr, the distance travelled by the woman before braking increases by a constant 3m.

The additional braking distance however, shares a nonlinear relationship with speed. With increasing speed, the braking distance travelled appears to increase at an even faster rate. The gradient of the curve becomes steeper and steeper, in contrast to the first line, where the constant slope gives it its linearity.  

...read more.

Middle

x1 = 32

x2 = 48

y1 = 6

y2 = 9

Gradient = y 2 – y 1  

image00.png

x 2 – x 1

= (9-6)

  (48-32)

= 3  (or 0.1875)

  16

3) So far, we have y = 0.1875x + c. To find the constant, we can plug in the coordinate (48,9) for x and y.

9 = (0.1875)(48) + c

9 = 9 + c

c = 0

4) The final function for speed versus thinking distance looks like this:

f(x) = (3/16)x + 0

When graphing the linear function and finding its equation through the “trendline” option on Excel, I initially obtained y = 3x + 3.

...read more.

Conclusion

y value (3). Excel considers the x-axis as ordinal instead of numerical. It ignores the fact that when speed is 0km/hr, thinking distance is naturally 0m (the line should pass through the origin but it does not).

Of course, this mistake could have been easily avoided on my part. Had I chosen a “scatter” instead of “line” graph, the numbers on the x-axis would have progressed by their true value of 16km/hr instead of 1km/hr. The instant “chart type” was changed to “scatter”, the trendline showed the correct equation of

y = 0.1875x.

...read more.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

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