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v1 Algebra, STD1 A1 2020 HSC 18

The distance, \(d\) metres, travelled by a car slowing down from \(u\) km/h to \(v\) km/h can be obtained using the formula

\(v^2=u^2-100 d\)

What distance does a car travel while slowing down from 100 km/h to 70 km/h?   (2 marks)

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\(51\ \text{metres}\)

Show Worked Solution

\(u=100 \ , \ v=70\)

\(v^2\) \(=u^2-100d\)
\(70^2\) \(=100^2-100d\)
\(100d\) \(=100^2-70^2\)
\(\therefore\ d\) \(=\dfrac{100^2-70^2}{100}\)
  \(=51\ \text{metres}\)