(i)[5]
Express $\frac{dv}{dt}$ in terms of $k$ and $v$, and hence show that $v = \frac{1}{4}(t - 6)^2$.
(ii)[4]
Find the distance covered by $P$ during the first $3$ seconds of its motion.
Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
Particle $P$, with mass $0.4\,\text{kg}$, travels in a straight line on a horizontal surface, and its velocity at time $t\,\text{s}$ is $v\,\text{m s}^{-1}$. A horizontal force of magnitude $k\sqrt{v}\,\text{N}$ acts against the motion of $P$. When $t = 0$, $v = 9$, and when $t = 2$, $v = 4$.
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This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Starts from differential equation $\frac{dv}{dt} = -2.5k\sqrt{v}$” …
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