4MA0 Higher January 2014 Paper 4R Q16
16 A particle moves from rest.
The speed of the particle is \(v\) m/s when it has moved a distance of \(x\) metres.
\(v\) is proportional to \(\sqrt{x}\)
When \(v = 8\), \(x = 25\)
(a) Express \(v\) in terms of \(x\). (3)
(b) Find the speed of the object when it has moved a distance of 56.25 metres. (2)
| Scheme | Marks |
|---|---|
| \(v = k\sqrt{x}\) oe | M1 |
| \(8 = k\sqrt{25}\) oe | M1 |
| \(v = 1.6\sqrt{x}\) oe | A1 |
| (3) |
Notes
A1: Allow \(v = k\sqrt{x}\) if \(k = 1.6\) is found in (a) or (b).
| Scheme | Marks |
|---|---|
| (\(v\) =) “1.6” \(\sqrt{56.25}\) | M1ft |
| 12 | A1 |
| (2) | |
| (5 marks) |
Notes
M1ft: Do not ft if \(k = 1\)
A1: cao