4MA0 Higher June 2016 Paper 3 Q14
14 A particle is moving along a straight line.
The fixed point \(O\) lies on this line.
The displacement of the particle from \(O\) at time \(t\) seconds is \(s\) metres where
\[s = 2t^3 - 12t^2 + 7t\](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 instantaneously zero. (2)
| Scheme | Marks |
|---|---|
| \(2 \times 3t^2\) ; \(-12 \times 2t\) ; 7 | M1 |
| \(6t^2 - 24t + 7\) | A1 |
| (2) |
Notes
M1: evidence of differentiation; at least two terms correct
| Scheme | Marks |
|---|---|
| \(6 \times 2t - 24 = 0\) | M1 |
| 2 | A1 |
| (2) |
Notes
M1: ft from a quadratic in (a) for correct differentiation and equating to zero
A1: ft