4400 Higher June 2008 Paper 4 Q19
19 A particle moves in a straight line through a fixed point \(O\).
The displacement of the particle from \(O\) at time \(t\) seconds is \(s\) metres, where\[s = t^2 - 6t + 10\]
(a) Find \(\dfrac{\mathrm{d}s}{\mathrm{d}t}\) (2)
(b) Find the velocity of the particle when \(t = 5\) (2)
(c) Find the acceleration of the particle. (2)
| Scheme | Marks |
|---|---|
| \(2t - 6\) | B1 B1 |
| (2) |
| Scheme | Marks |
|---|---|
| \(2 \times 5 - 6\) | M1f |
| 4 | A1 |
| (2) |
Notes
M1f: Sub \(t = 5\) in “\(\mathrm{d}s/\mathrm{d}t\)” dep on linear f(\(t\))
M0 for \((2 \times 5 - 6)/5\)
A1: Cao
| Scheme | Marks |
|---|---|
| \(\mathrm{d}(\text{“}2t - 6\text{”})/\mathrm{d}t\) | M1 |
| 2 | A1 |
| (2) | |
| (6 marks) |
Notes
M1: Attempt diff “\(\mathrm{d}s/\mathrm{d}t\)” dep on linear f(\(t\))
A1: Cao