A-LevelMathematicsMechanics9709/51 · May/June 2018 · Q37 Marks
A particle P of mass 0.4 kg is projected horizontally along a smooth horizontal plane from a point O. At time t s after projection the velocity of P is v m s¯¹. A force of magnitude 0.8t N directed away from O acts on P and a force of magnitude 2e¯ᵗ N opposes the motion of P.
- (i)Show that dv/dt = 2t - 5e⁻ᵗ.[2]
- (ii)Given that v = 8 when t = 1, express v in terms of t.[3]
- (iii)Find the speed of projection of P.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- [M1] 0.4 dv/dt = 0.8t – 2e¯ᵗ; Use Newton's Second Law horizontally
- [A1] dv/dt = 2t - 5e¯ᵗ; AG
- [M1] ∫dv = ∫(2t – 5e¯ᵗ)dt; Attempt to integrate the equation from part (i)
- [M1] t = 1 and v = 8 so c = 5.16; Attempt to find the constant of integration, c
- [A1] v = t² + 5e¯ᵗ + 5.16 or v = t² + 5e¯ᵗ + 7 – 5e⁻¹
- [M1] Evaluates v for t = 0
- [A1] V = 10.2 ms¯¹
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