4400 Higher November 2009 Paper 4 Q19
19 A particle moves in a straight line through a fixed point \(O\).
The displacement, \(s\) metres, of the particle from \(O\) at time \(t\) seconds is given by \[s = t^3 - 5t^2 + 8\]
(a) Find an expression for the velocity, \(v\) m/s, of the particle after \(t\) seconds. (2)
(b) Find the time at which the acceleration of the particle is 20 m/s2. (2)
| Scheme | Marks |
|---|---|
| \(3t^2 - 10t\) | B2 |
| (2) |
Notes
B2: B1 for \(3t^2\) or \(-10t\)
Ignore further differentiation seen in body or on answer line
| Scheme | Marks |
|---|---|
| \(6t - 10 = 20\) | M1 |
| 5 | A1 |
| (2) | |
| (4 marks) |
Notes
M1: for linear expression including either \(6t\) or \(-10\)
A1: ft from “\(6t - 10\)” = 20 if M1 scored