# Finding the acceleration of Block attached using tricky string setup

Below shown is a setup, and block B starts from rest and moves towards right with a constant acceleration. Does the acceleration differ for the blocks ? I am a bit confused because of the tricky string setup. If after time t, the velocity of A with respect to B becomes v, then what would be the acceleration of A ?

My understanding is : After time t, Block B will be brought to rest instantaneously resulting in non-zero relative velocity which otherwise will continue to be 0.

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I do not think it is that tricky. For each pulley you have an equation relating the speed of the rope in, the speed of the rope out and the speed of the pivot. The speed of the pivot is the average of the two speed ropes.

Here are the kinematics of the system

$$v_E = 0 \\ v_B = a t \\ v_C = v_B \\ v_B = \frac{v_D+v_E}{2} \\ v_A = \frac{v_C+v_D}{2}$$

If you notice there are five equations, with five unknowns ($v_A$, $v_B$, $v_C$, $v_D$, $v_E$).

$$v_A = \frac{3}{2} v_B \\ v_B = a t \\ v_C = 0 \\ v_D = 2 v_B \\ v_E = 0$$