June 2025 Paper 2 Q13
13 A car moves, in a straight line on a horizontal road, from a point \(A\) to a point \(B\)
The distance \(AB\) is 225 metres.
At the point \(B\), the velocity of the car is \(30\ \text{m s}^{-1}\)
The car is modelled as having a constant acceleration of \(2\ \text{m s}^{-2}\)
(a) Show that the car starts from rest at point \(A\) [2 marks]
(b) The car continues to move past the point \(B\) in the same straight line.
Explain why the model would eventually become invalid.
[1 mark]| Scheme | Marks | AO |
|---|---|---|
| Substitutes \(a = 2\) \(s = 225\), \(v = 30\) and \(u\) into \(v^2 = u^2 + 2as\) OE | M1 | 3.3 |
| Completes reasoned argument, with at least one intermediate step after the initial substitution, to obtain \(u = 0\) or \(u^2 = 0\) and concludes the car starts from rest AG Accept making \(u\) the subject of \(v^2 = u^2 + 2as\) before substitution as the intermediate step | R1 | 2.1 |
| (2) |
Typical solution
\[a = 2 \quad s = 225, \quad v = 30\]\[v^2 = u^2 + 2as\]\[30^2 = u^2 + 2 \times 2 \times 225\]\[900 = u^2 + 900\]\[u^2 = 0\]\[u = 0\ \text{m s}^{-1}\]Therefore, the car is at rest at point \(A\).
| Scheme | Marks | AO |
|---|---|---|
| Explains why the model becomes invalid, eg: • That acceleration is unlikely to remain constant Or gives a contextual reason as to why the car may have to slow down or stop, eg: • That the car reaches its maximum speed • The road will not remain straight or there will be an obstacle • The car will run out of fuel | E1 | 3.5b |
| (1) | ||
| (3 marks) |
Typical solution
A car’s acceleration is unlikely to stay at the same rate.