The table shows data for a car stopping on a wet road.

v d

20 38

30 86

40 153

stopping distance formula d (v) = 2.15v2/64.4f

Determine the value of f, rounded to the nearest hundredth.

First, rearrange the formula to make 'f' the subject

d (v) = 2.15v^2 : 64.4f

64.4f = 2.15v^2 : d (v)

f = 2.15v^2 : 64.4d (v)

When d (v) = 38 and v = 20

f = 2.15 (20) ^2 : 64.4 (38)

f = 0.35

When d (v) = 86 and v = 30

f = 2.15 (30) ^2 : 64.4 (86)

f = 0.35

When d (v) = 153 and v = 40

f = 2.15 (40) ^2 : 64.4 (153)

f = 0.35

So f is a constant 0.35