A-LevelMathematicsMechanics9709/42 · Oct/Nov 2024 · Q15 Marks

The velocity of a particle moving in a straight line at time t seconds after leaving a fixed point O is vms⁻¹. The diagram shows a velocity-time graph which models the motion of the particle from t = 0 to t = T. The graph consists of four straight line segments. The particle accelerates from rest to a speed of V ms⁻¹ over a period of 4 s, and then decelerates at 5/3 ms⁻² to instantaneous rest over a period of 6 s. The particle then travels back towards O, reaching a maximum speed of 3 ms⁻¹ before coming to rest at time t = T. [Figure 1]

(a)Find the value of V.[2]
(b)Given that the total distance travelled by the particle from t = 0 to t = T is 68m, find the value of T.[3]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

[M1] Use of v=u+at or use of acceleration is gradient of the line
[A1] Make sure that 10 comes from a correct initial equation or equivalent, if not then A0, e.g. (0-V)/(10-4) = 5/3 leading to V=10 is M1A0.
[B1FT] SOI [If correct distance is 50 m.]
[M1] Use distance (68) is total area under graph. Their 50 must be from 5*their|V|. Allow with -3. Allow 1/2*X*3 + 1/2*10*their|V|=68 and use of T=X+10.
[A1] WWW

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