A-LevelMathematicsMechanics9709/51 · Oct/Nov 2019 · Q36 Marks
A smooth horizontal surface has two fixed points O and A which are 0.8 m apart. A particle P of mass 0.25 kg is projected with velocity 3 m s¯¹ horizontally from A in the direction away from O. The velocity of P is v m s¯¹ when the displacement of P from O is x m. A force of magnitude kv²x⁻² N opposes the motion of P.
- (i)Show that v dv/dx = -4kv²x⁻².[1]
- (ii)Express v in terms of k and x.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.
- [B1] AG
- [M1] Attempt to integrate
- [A1] ln v = 4k/x (+c)
- [A1] Finds c (x=0.8, v=3 hence c = ln3 – 5k)
- [M1] ln v = 4k/x + ln 3 – 5k
- [A1] v = 3 e^((4k-5k)/x)
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