How to Calculate the Speed of M2 in a Pulley System After 1.35 Seconds?

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To calculate the speed of M2 after 1.35 seconds in a frictionless pulley system with masses M1 = 3.0 kg, M2 = 7.0 kg, and M3 = 5.0 kg, the relevant equation is V = Vo + at, where Vo is the initial velocity (0 in this case). The acceleration (a) needs to be determined, and it is noted that the accelerations of all blocks are equal (a1 = a2 = a3). The user is seeking guidance on how to find the acceleration using the forces acting on the system. Understanding the forces and applying Newton's second law will help in calculating the acceleration and subsequently the speed of M2.
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Homework Statement



The three blocks shown are relased at t=0 from the position shown in the figure. Assume that there is no friction between the table and M2, and that the two pulleys are massless and frictionless. The masses are: M1 = 3.0 kg, M2 = 7.0 kg, M3 = 5.0 kg.

Calculate the speed of M2 at a time 1.35 s after the system is released from rest.

http://nplq1.phyast.pitt.edu/res/msu/physicslib/msuphysicslib/09_Force_and_Motion/graphics/prob81_pulley2

Homework Equations


I figure I need an equation with time like V= Vo +at and then I also need to use an equation to solve for a. I know all of the a's are equal (a1=a2=a3), yet I do not know which equation to use.


3. The Attempt at a Solution
for the first equation I plugged in V=Vo +at, t was the 1.35s, Vo = 0, v is unknown, and a I am unsure how to get still? Could you please help me out?
 
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