A-LevelMathematicsMechanics9709/42 · Oct/Nov 2019 · Q25 Marks

The diagram shows a velocity-time graph which models the motion of a tractor. The graph consists of four straight line segments. The tractor passes a point O at time t = 0 with speed U m s⁻¹. The tractor accelerates to a speed of V m s⁻¹ over a period of 5 s, and then travels at this speed for a further 25 s. The tractor then accelerates to a speed of 12m s⁻¹ over a period of 5 s. The tractor then decelerates to rest over a period of 15 s. [Figure 2.1]

(i)Given that the acceleration of the tractor between t = 30 and t = 35 is 0.8 ms⁻², find the value of V.[2]
(ii)Given also that the total distance covered by the tractor in the 50 seconds of motion is 375 m, find the value of U.[3]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

[M1] Use gradient of graph or constant acceleration formulae to set up an equation in V
[A1] V = 8
[M1] Attempt to find total distance travelled by the tractor in 50s to set up an equation for U using EITHER areas OR suvat equations OR a combination of areas and suvat. In either case total distance must be attempted
[A1FT] Correct equation FT on their V from (i)
[A1] U = 6

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.