June 2024 Paper 2 Q14
14 The displacement, \(r\) metres, of a particle at time \(t\) seconds is
\[r = 6t - 2t^2\](a) Find the value of \(r\) when \(t = 4\) [1 mark]
(b) Determine the range of values of \(t\) for which the displacement is positive. [2 marks]
| Scheme | Marks | AO |
|---|---|---|
| Obtains \(-8\) | B1 | 1.1b |
| (1) |
Typical solution
\(-8\)
| Scheme | Marks | AO |
|---|---|---|
| Forms an equation or inequality to compare \(6t - 2t^2\) with 0 PI by \(6t = 2t^2\), \(6t \gt 2t^2\) or \(t\) = 0 and \(t\) = 3 | M1 | 3.1a |
| Obtains \(0 \lt t \lt 3\) OE | A1 | 1.1b |
| (2) | ||
| (3 marks) |
Typical solution
\[-2t^2 + 6t \gt 0\]So \(0 \lt t \lt 3\)