A-LevelMathematicsMechanics9709/42 · Oct/Nov 2021 · Q14 Marks

The diagram shows a velocity-time graph which models the motion of a car. The graph consists of six straight line segments. The car accelerates from rest to a speed of 20 ms⁻¹ over a period of 5 s, and then travels at this speed for a further 20s. The car then decelerates to a speed of 6 ms⁻¹ over a period of 5 s. This speed is maintained for a further (T – 30) s. The car then accelerates again to a speed of 20 m s⁻¹ over a period of (50 – T) s, before decelerating to rest over a period of 10 s. [Diagram]

(a)Given that during the two stages of the motion when the car is accelerating, the accelerations are equal, find the value of T.[2]
(b)Find the total distance travelled by the car during the motion.[2]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

M1 Equate the accelerations and set up an equation in T. Allow correct use of their incorrect 20/5
A1 T = 46.5
M1 Attempt to find the total distance travelled using areas. Allow with T not yet substituted. Allow one error in use of area formulae or omission of only one of the areas: 0-5, 5–25, 25–30, 30–T, T-50, 50--60.
A1 FT FT their T value: Provided 30 <T < 50 and distance = 1085-7T
Total distance travelled = 759.5 m

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