O-LevelPhysicsForces5054/21 · Oct/Nov 2025 · Q18 Marks
A car is at rest on a straight horizontal road. At time t = 0, the car begins to accelerate. Fig. 1.1 shows how the momentum of the car varies with time. [Figure 1.1]
- (a)Use Fig. 1.1 to determine the resultant force acting on the car during the first 1.5s of its motion.[3]
- (b)(i)When the momentum of the car is p, its kinetic energy is Ek. Show that p^2 / 2m = Ek[2]
- (b)(ii)At t = 6.0 s, the kinetic energy of the car is 5.4 × 10^5 J. Use Fig. 1.1 to determine the momentum p of the car at t = 6.0s, and use the equation in (b)(i) to determine the mass m of the car. Show your working.[3]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.
- [C1] (change in momentum / momentum =) 18 000 (kgm/s)
- [C1] (force =) change in momentum / time taken or 18 000 / 1.5
- [A1] 12 000 (N)
- [B1] p² / 2m = m²v² / 2m
- [B1] shown to be ½mv² (and equal to Ek / kinetic energy)
- [B1] Ek = ½mv² seen
- [B1] 39 000 seen
- [C1] (m =) 39 000² / (2 × 5.4 × 10⁵)
- [A1] 1400 (kg)
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