Find Acceleration of Blocks A & B | Homework Statement

[mashac]

Homework Statement

Question:

2 Blocks A and B are resting on a horizontal plane and connected by a cord as shown in figure. The Block A starts from rest and moves to the left with constant acceleration.It was observed that the Block B attains a velocity of 12 m/s after moving a distance of 24 m.
Find acceleration of Blocks A & B.


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Homework Equations

The Attempt at a Solution

In the solution there is an equation 3*accel of B+2*accel of A=0. I didn't understand this equation and the reason for using it. Is it a special property of cord? .I know how to find accel of Block B but to find accel of Block A this equation is used. Please, explain me about this equation and in what situations it is used.

 

[gneill]

Note that the cord is of a fixed total length. Also note that the cord is anchored at a fixed location on the "floor". If you set up your coordinate system so that this anchor point is the origin, then you can, using the fact that the cord length is fixed, derive a relationship between the position of block A and the position of block B.

The derivative of position is velocity. The derivative of velocity is acceleration. Your mystery relationship will pop out of the process.

 

[Quinzio]

You can "cut" the cord near the object, and this will give you a divider for its movements.
Counting the way the red line cuts the cord near the objects.

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