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Functions, 2ADV EQ-Bank 12

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.

  1. Find the value of `k`.   (2 marks)

    --- 4 WORK AREA LINES (style=lined) ---

  2. What is the braking distance when the speed of the car is 90 km/h?   (1 mark)

    --- 2 WORK AREA LINES (style=lined) ---

Show Answers Only

a.    `k=0.008`

b.    `64.8\ text{m}`

Show Worked Solution

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}`

Filed Under: Direct and Inverse Variation Tagged With: Band 3, smc-6383-10-\(\propto kx^{n}\), smc-6383-40-Stopping Distance

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