M1 June 2005 Q1
1. In taking off, an aircraft moves on a straight runway \(AB\) of length 1.2 km. The aircraft moves from \(A\) with initial speed 2 m s\(^{-1}\). It moves with constant acceleration and 20 s later it leaves the runway at \(C\) with speed 74 m s\(^{-1}\). Find
(a) the acceleration of the aircraft, (2)
(b) the distance \(BC\). (4)
| Scheme | Marks |
|---|---|
| ‘\(v = u + at\)’: \(74 = 2 + a \times 20 \;\Rightarrow\; a = 3.6\) m s\(^{-2}\) | M1 A1 |
| (2) |
| Scheme | Marks |
|---|---|
| ‘\(v^2 = u^2 + 2as\)’: \(74^2 = 2^2 + 2 \times 3.6 \times AC\) or ‘\(s = ut + \tfrac{1}{2}at^2\)’: \(AC = 2 \times 20 + \tfrac{1}{2} \times 3.6 \times 20^2\) | M1 A1ft |
| \(\Rightarrow AC = 760\) m | A1 |
| Hence \(BC = 1200 - 760 = 440\) m | B1ft |
| (4) | |
| (6 marks) |