June 2025 Paper 3 Mechanics Q1
1. A car moves in a straight line along a horizontal road with constant acceleration \(2\ \text{m s}^{-2}\)
The car is moving with speed \(15\ \text{m s}^{-1}\) in the direction of the acceleration when it passes a signpost on the road.
The car is modelled as a particle.
Figure 1 below shows the horizontal forces acting on the car.
Given that
- the car has mass 800 kg
- the driving force of the engine has magnitude \(D\) newtons
- the resistance to the motion of the car has magnitude 400 N
- the acceleration of the car is \(2\ \text{m s}^{-2}\) in the direction of the driving force
| Scheme | Marks | AO |
|---|---|---|
| \(v = 15 + (2 \times 4)\) | M1 | 3.1b |
| \(= 23\ (\text{m s}^{-1})\) | A1 | 1.1b |
| (2) |
Notes
M1: Use of \(v = u + at\) or any other complete method to form an equation in \(v\) only. Condone sign errors.
e.g. May find \(s\) first: \(s = (15 \times 4) + \dfrac{1}{2} \times 2 \times 4^2 = 76\) then
either: \(76 = 4v - \dfrac{1}{2} \times 2 \times 4^2\)
or: \(76 = \dfrac{(15 + v)}{2} \times 4\)
or: \(v^2 = 15^2 + 2 \times 2 \times 76\)
N.B. If they use \(v = u + at\) and have \(15 = u + (2 \times 4)\), M1A0
M0 if they clearly use an incorrect suvat formula or \(u = 0\)
A1: cao. Must be positive.
A0 if they get 23 but go on and do something with it. i.e. not ISW
N.B. 23 with no working can score both marks.
| Scheme | Marks | AO |
|---|---|---|
| \(D - 400 = 800 \times 2\) | M1 | 3.1b |
| \((D =)\ 2000\) | A1 | 1.1b |
| (2) | ||
| (4 marks) |
Notes
M1: Use of \(F = ma\) to form an equation in \(D\) or a complete expression for \(D\), with correct number of terms, condone sign errors and \(g\) in the \(ma\) term.
A1: cao
N.B. 2000 with no working can score both marks.