Example 12.4 A metallic particle is subjected to the influence of a magnetic field as it travels downward through a fluid that extends from plate $A$ to plate $B$. If the particle is released from rest at the midpoint $C, s=100 \mathrm{~mm}$, and the acceleration is a $=(4 s) \mathrm{m} / \mathrm{s}^{2}$, where $s$ is in meters, determine the velocity of the particle when it reaches plate $B, s=200 \mathrm{~mm}$, and the time it takes to travel from $C$ to $B$. Solution: \[ \begin{array}{l} a=45 \mathrm{~m} / \mathrm{s}^{2} \\ S_{0}=100 \mathrm{~mm}=0.1 \mathrm{~m} \\ V_{0}=0 \mathrm{~m} / \mathrm{s} \end{array} \] \[ V_{0}=0 \mathrm{~m} / \mathrm{s} \] \[ \text { obefound } \begin{array}{r} V_{B}=\text { ? } \\ t_{B}=\text { ? } \end{array} \] \[ a=\frac{d v}{1 t} \sqrt{v a d s}=v d v \]

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