M2 June 2006 Q1
1. A particle \(P\) moves on the \(x\)-axis. At time \(t\) seconds, its acceleration is \((5 - 2t)\) m s\(^{-2}\), measured in the direction of \(x\) increasing. When \(t = 0\), its velocity is 6 m s\(^{-1}\) measured in the direction of \(x\) increasing. Find the time when \(P\) is instantaneously at rest in the subsequent motion. (6)
| Scheme | Marks |
|---|---|
| \(a = 5 - 2t\ \ \Rightarrow\ \ v = 5t - t^2, + 6\) | M1 A1, A1 |
| \(v = 0\ \Rightarrow\ t^2 - 5t - 6 = 0\) indep | M1 |
| \((t - 6)(t + 1) = 0\) dep | M1 |
| \(t = \underline{6\ \text{s}}\) | A1 |
| (6) | |
| (6 marks) |