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Year 12 Specialist (Unit 3 & 4) Modelling motion

Differential equations of the form v=f(x) and a=f(v)

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Questions
Question 1
163471

A particle moves in a line such that the velocity, \(\dot{x} \text{ m} / \text{s}\), is given by \(\dot{x}=\frac{1}{x+4}, x>0\). If \(x=0\) when \(t=0\), find:
i) \(t\) when \(x=4\).
ii) \(x\) when \(t=10\).

i) \(t = 24 \text{ s}\)
ii) \(x = 2 \text{ m}\)

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