October 2021 Paper 3 Q9
9 There are three checkpoints, \(A\), \(B\) and \(C\), in that order, on a straight horizontal road. A car travels along the road, in the direction from \(A\) to \(C\), with constant acceleration. The car takes \(20\,\mathrm{s}\) to travel from \(B\) to \(C\). The speed of the car at \(B\) is \(14\,\mathrm{m\,s^{-1}}\) and the speed of the car at \(C\) is \(18\,\mathrm{m\,s^{-1}}\).
(a) Find the acceleration of the car. [1]
It is given that the distance between \(A\) and \(B\) is \(330\,\mathrm{m}\).
(b) Determine the speed of the car at \(A\). [2]
| Scheme | Marks | AO |
|---|---|---|
| \(18 = 14 + 20a \Rightarrow a = 0.2\ \left(\mathrm{m\,s^{-2}}\right)\) | B1 | 1.1 |
| [1] |
| Scheme | Marks | AO |
|---|---|---|
| \(14^2 = u^2 + 2(0.2)(330)\) | M1 | 3.3 |
| \(u = 8\ \left(\mathrm{m\,s^{-1}}\right)\) | A1 | 1.1 |
| [2] |
Notes
M1: Use of SUVAT equation to determine \(u\) with their \(a\) or other complete method to find \(u\)
M0 if using 18 for \(v\)