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The braking distance of a car, in metres, is directly proportional to the square of its speed in km/h, and can be represented by the equation
`text{braking distance}\ = k xx text{(speed)}^2`
where `k` is the constant of variation.
The braking distance for a car travelling at 50 km/h is 20 m.
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a. `k=0.008`
b. `64.8\ text{m}`
a. `text{braking distance}\ = k xx text{(speed)}^2`
| `20` | `=k xx 50^2` | |
| `k` | `=20/50^2=0.008` |
b. `text{Find}\ d\ text{when speed = 90 km/h:}`
`d=0.008 xx 90^2=64.8\ text{m}`
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)`
`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)` |