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Year 12 Maths Extension 2 (2027) Mechanics

Rectilinear Resisted Motion

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Question 1
183591
A particle of mass \(1\) kg is projected along a smooth horizontal surface with speed \(10\ \text{ms}^{-1}\). It experiences a resistance of \(2v\) N, where \(v\) is its speed. Find \(v\) as a function of time \(t\).
dv/dt=-2v; ln v = -2t + C; v=10 at t=0 gives v = 10 e^-2t.

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