M1 January 2009 Q1
1. A particle \(P\) moves with constant acceleration \((2\mathbf{i} - 5\mathbf{j})\) m s\(^{-2}\). At time \(t = 0\), \(P\) has speed \(u\) m s\(^{-1}\). At time \(t = 3\) s, \(P\) has velocity \((-6\mathbf{i} + \mathbf{j})\) m s\(^{-1}\).
Find the value of \(u\). (5)
| Scheme | Marks |
|---|---|
| \(-6\mathbf{i} + \mathbf{j} = \mathbf{u} + 3(2\mathbf{i} - 5\mathbf{j})\) | M1 A1 |
| \(\Rightarrow\ \mathbf{u} = -12\mathbf{i} + 16\mathbf{j}\) | A1 cso |
| \(\Rightarrow\ u = \sqrt{(-12)^2 + 16^2} = 20\) | M1 A1 |
| (5 marks) |