Higher June 2019 Paper 1R Q16
16 A particle \(P\) is moving along a straight line.
The fixed point \(O\) lies on this line.
At time \(t\) seconds, the displacement, \(s\) metres, of \(P\) from \(O\) is given by
At time \(t\) seconds, the velocity of \(P\) is \(v\) m/s.
(a) Find an expression for \(v\) in terms of \(t\). (2)
(b) Find the time at which the acceleration of the particle is 6 m/s2 (3)
| Scheme | Marks |
|---|---|
| \(3 \times 4t^2 - 2 \times 6t + 5\) | M1 |
| \(12t^2 - 12t + 5\) | A1 |
| (2) |
Notes
M1: For 2 terms correct
A1: Fully correct
| Scheme | Marks |
|---|---|
| \(24t - 12\) | M1 |
| \(\text{``}{24t - 12}\text{''} = 6\) | M1 |
| 0.75 | A1 |
| (3) | |
| (5 marks) |
Notes
M1: Method to differentiate their \(v\), ft a 3 term quadratic expression from (a)
M1: ft if previous M1 awarded
A1: oe