A particle $P$ with mass $0.35\text{ kg}$ is fastened to the midpoint of a light elastic string whose natural length is $4\text{ m}$. The two ends of the string are fixed at points $A$ and $B$, which are $4.8\text{ m}$ apart and lie at the same horizontal height. In equilibrium, $P$ hangs at a point $0.7\text{ m}$ vertically beneath the midpoint $M$ of $AB$ (see diagram).
(i)[4]
Determine the tension in the string, and hence deduce that the modulus of elasticity of the string is $25\text{ N}$.
(ii)[6]
Find the speed of $P$ as it passes through $M$.
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