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 = 2m 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, s (m)

1.5

8

14

28

Speed, u (m s-1)

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.