Rates of Change, SMB-006

The stopping distance of a car on a certain road, once the brakes are applied, is directly proportional to the square of the speed of the car when the brakes are first applied.

A car travelling at 70 km/h takes 58.8 metres to stop.

How far does it take to stop if it is travelling at 105 km/h? (3 marks)

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`132.3\ text(metres)`

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`text(Let)\ \ d\ text(= stopping distance)`

`d prop s^2`

`d = ks^2`

`text(Find)\ k,`

`58.8`	`= k xx 70^2`
`k`	`= 58.8/(70^2)`
	`= 0.012`

`text(Find)\ d\ \ text(when)\ s = 105:`

`d`	`= 0.012 xx 105^2`
	`= 132.3\ text(metres)`