University of the West of England

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**
Linearisation using change of variable** (car
skid distance)

Link to Video Answer

A vehicle
skidding to a halt from an initial speed, *u* (m s^{-1}), will stop
in a distance, *s *(m), given by the equation: *u *^{2 }= 2*m
g s*,
where *g* = 9.81 m s^{-2}, and *
m*
is the coefficient of friction between the tyres and the road.
The stopping
distances, *s*, are measured experimentally for different initial speeds,
*u*, and recorded in the following table:

Distance, |
1.5 |
8 |
14 |
28 |

Speed, |
5 |
10 |
15 |
20 |

Use Excel to
perform a process of linearisation to calculate a best-estimate for the value of
the coefficient of friction, *
m*.

i) Discuss whether your ‘linearised’ line of best fit should pass through the origin of your graph.

ii)
Calculate the best-estimate value for *
m*.