A-LevelMathematicsMechanics9709/52 · Oct/Nov 2017 · Q36 Marks
A particle P of mass 0.4 kg is released from rest at a point O on a smooth plane inclined at 30° to the horizontal. P moves down the line of greatest slope through O. The velocity of P is v ms⁻¹ when its displacement from O is x m. A retarding force of magnitude 0.2v² N acts on P in the direction PO.
- (i)Show that v dv/dx = 5 - 0.5v².[2]
- (ii)Express v in terms of x.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- [M1] Uses Newton's Second Law down the plane. Allow a for vdv/dx.
- [A1] vdv/dx = 5 - 0.5 v² AG
- [M1] Separates the variables and attempts to integrate.
- [A1] -ln(5 – 0.5 v² ) = x (+ c )
- [M1] Puts x = 0, v =0 to find c and attempts to solve for v.
- [A1] v = √(10-10e⁻ˣ)
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