(i)[5]
By working through a suitable differential equation, show that v = (27 - 9x)^{\frac{2}{3}}.
(ii)[4]
Calculate x when t = 0.5.
Mathematics 9709 · AS & A Level · Probability
Probability — practice question
A particle P of mass 0.5 kg travels in a straight line across a smooth horizontal plane. At time t s, P has displacement x m from a chosen point on the line, and its velocity is v m s^{-1}. It is given that when t = 0, x = 0 and v = 9. The motion of P is resisted by a force of magnitude 3√v N.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies Newton’s second law together with a = v\dfrac{dv}{dx} to obtain 0.5v\dfrac{dv}{dx} = -3v^{\frac{1}{2}}” …
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