A-LevelMathematicsMechanics9709/42 · Oct/Nov 2025 · Q13 Marks
The diagram shows the displacement-time graph for the motion of a particle. The particle starts from rest at a point O and travels with constant acceleration a m s⁻², taking 4 s to move a distance of x m. The particle then returns to O with constant speed of 40 m s⁻¹, over a period of 2 s. [Figure 1]
- Find the value of x and the value of a.[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.
- [M1] Any method to find x, or a or getting an equation relating x and a; Condone assumption that speed is 40 at the end of first phase of motion. Allow e.g. x = ½×4×40, x= ½(0+40)×4, 40²=0²+2ax, a= (40-0)/4, x=40×4- ½×a×4².
- [A1] x = 80; CWO. Must be x = ... M1A0 for those who have (x-0)/(4-6) = 40 and have x = -80 followed by x=80 without any explanation.
- [A1] a = 10; CWO.
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