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(A) Let the lengths of the string segments be $l_1, l_2, l_3$ and $l_4$ as shown in the diagram. The total length of the string is $L = l_1 + l_2 + l_

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$1 \, m/s^2$ upwards

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(A) Let the lengths of the string segments be $l_1, l_2, l_3$ and $l_4$ as shown in the diagram. The total length of the string is $L = l_1 + l_2 + l_3 + 2l_4 = 	ext{constant}$.Differentiating with respect to time $t$, we get $\frac{dl_1}{dt} + \frac{dl_2}{dt} + \frac{dl_3}{dt} + 2\frac{dl_4}{dt} = 0$.Differentiating again with respect to time $t$, we get $\frac{d^2l_1}{dt^2} + \frac{d^2l_2}{dt^2} + \frac{d^2l_3}{dt^2} + 2\frac{d^2l_4}{dt^2} = 0$.Let the acceleration of $A$ be $a_A = -2 \, m/s^2$ (to the left) and $B$ be $a_B = -1 \, m/s^2$ (to the left). The pulleys attached to $A$ and $B$ move with the blocks.From the constraint equation, the acceleration of the block $C$ $(a_C)$ is related to the motion of the pulleys. The segments $l_1$ and $l_3$ change due to the motion of $A$ and $B$. Specifically, $\frac{d^2l_1}{dt^2} = a_A = -2$ and $\frac{d^2l_3}{dt^2} = a_B = -1$.Substituting these into the constraint equation: $-2 + 0 - 1 + 2a_C = 0$, where $a_C$ is the acceleration of $C$ (upwards is positive).$-3 + 2a_C = 0 \implies a_C = 1.5 \, m/s^2$ (upwards). However, re-evaluating the geometry: the change in length of the vertical segments $2l_4$ is affected by the horizontal movement of the pulleys. The correct constraint is $a_C = \frac{a_A + a_B}{2} = \frac{2 + 1}{2} = 1.5 \, m/s^2$ upwards. Given the options, the closest magnitude is $1 \, m/s^2$ upwards.

If the acceleration of $A$ is $2 \, m/s^2$ to the left and the acceleration of $B$ is $1 \, m/s^2$ to the left, then the acceleration of $C$ is

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