M1 June 2010 Q1
1. A particle \(P\) is moving with constant velocity \((-3\mathbf{i} + 2\mathbf{j})\) m s\(^{-1}\). At time \(t = 6\) s \(P\) is at the point with position vector \((-4\mathbf{i} - 7\mathbf{j})\) m. Find the distance of \(P\) from the origin at time \(t = 2\) s. (5)
| Scheme | Marks |
|---|---|
| \((-4\mathbf{i} - 7\mathbf{j}) = \mathbf{r} + 4(-3\mathbf{i} + 2\mathbf{j})\) | M1 A1 |
| \(\mathbf{r} = (8\mathbf{i} - 15\mathbf{j})\) | A1 |
| \(|\mathbf{r}| = \sqrt{8^2 + (-15)^2} = 17\) m | M1 A1 ft |
| (5 marks) |