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If the rope is drawn toward the motor M at a speed of {v}_{M} = (5{t}^{3/2}) m/s , where t is in seconds, determine the speed of cylinder A when t = 1 s .

Step-by-step

position Coordinates: By referring to Fig. a, the length of the rope written in terms of the position coordinates s_{A} and s_{M} is

3 s_{A}+s_{M}=l

Time Derivative: Taking the time derivative of the above equation,
(+\downarrow)         3 v_{A}+v_{M}=0
Here, v_{M}=\left(5 t^{3 / 2}\right) m/s. Thus,

3 v_{A}+5 t^{3 / 2}=0
v_{A}=\left(-\frac{5}{3} t^{3 / 2}\right) m/s=\left(\frac{5}{3} t^{3 / 2}\right) m /\left .s\right|_{t=1 s}=1.67 m/s

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