4MA0 Higher June 2013 Paper 3R Q19
19 A particle is moving in a straight line which passes through a fixed point \(O\).
The displacement, \(s\) metres, of the particle from \(O\) at time \(t\) seconds is given by
(a) Find an expression for the velocity, \(v\) m/s, of the particle at time \(t\) seconds. (2)
(b) Find the time at which the acceleration of the particle is zero. (2)
| Scheme | Marks |
|---|---|
| \((v =)\ 18t - 3t^2\) | B2 |
| (2) |
Notes
B2: for \(18t - 3t^2\) oe seen as final answer
B1 for \(18t\) or \(3t^2\) or \(-3t^2\)
| Scheme | Marks |
|---|---|
| \((a =)\ \text{“}18 - 6t\text{”}\ (=0)\) | M1ft |
| \((t =)\ 3\) | A1ft |
| (2) |
Notes
M1ft: ft if differentiating correctly a quadratic with 2 or 3 terms