2025 Paradigm Sec 3 Mock EOY Q14

2025 Paradigm Sec 3 Mock EOY Q14

Secondary 3
9 marks

[Linear Law]

An experiment is conducted to find the distance, \(s\) metres, travelled by an object over time, \(t\) seconds. The table below shows the corresponding values of \(t\) and \(s\).

\(t\)\(1.0\)\(1.5\)\(2.0\)\(2.5\)\(3.0\)\(3.5\)
\(s\)\(4.20\)\(4.65\)\(5.09\)\(5.50\)\(5.89\)\(6.25\)

It is known that \(s\) and \(t\) are related by the equation \(s=a\sqrt t+\dfrac b{\sqrt t}\), where \(a\) and \(b\) are constants.

  1. On the grid below, plot \(s\sqrt t\) against \(t\) and draw a straight line.[2]
  2. Use your graph to estimate \(a\) and \(b\).[4]
  3. By drawing a suitable straight line on your graph, find the value of \(t\) that satisfies the equation \(2s\sqrt t+2t-10=at+b\).[3]

Solution:

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Answer:(b) \(a\approx3.00\), \(b\approx1.20\); (c) \(t\approx1.76\text{ s}\) (graphical estimate).

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