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Algebra, STD2 A4 2023 HSC 22 (Adapted)

The stopping distance of a motor bike, in metres, is directly proportional to the square of its speed in km/h, and can be represented by the equation

`text{stopping distance}\ = k xx text{(speed)}^2`

where `k` is the constant of variation.

The stopping distance for a motor bike travelling at 40 km/h is 16 m.

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

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

  2. What is the stopping distance when the speed of the motor bike is 80 km/h?   (1 mark)

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

Show Answers Only

a.    `k=0.01`

b.    `64.0\ text{m}`

Show Worked Solution

a.  `text{stopping distance}\ = k xx text{(speed)}^2`

`16` `=k xx 40^2`  
`k` `=16/40^2=0.001`  

 
b.    `text{Find stopping distance}\ (d)\ text{when speed = 80 km/h:}`

`d=0.01 xx 80^2=64.0\ text{m}`

Filed Under: Non-Linear: Exponential/Quadratics (Std 2-X), Quadratic Relationships (Y12-X) Tagged With: adapted, Band 4, smc-7720-40-Proportional

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