When a problem involves multiple objects connected together by a constraint such as a rope, we take the rope to be massless and inextensible and analyze the forces on each of the objects separately. It is important to choose a direction which will be positive and to define all vector quantities as positive or negative with respect to that direction for the entire problem. We are free to choose this positive direction and the reference point for zero gravitational potential energy as well. We will denote the tension in the massless rope by T.
In this problem we have a cart on a table which is connected by a rope over a pulley to a hanging block. We will choose the negative direction to be to the left and then over the pulley and down. That is to say that, for the cart, a negative velocity will mean that the cart is moving to the left, and for the hanging block, a negative velocity will mena that it is falling.
In the following, we will derive the acceleration of the system of block:
Let the hanging block be m1, and the block on the table be m2.
The net force will be the weight of m1 minus the force of friction of m2.
weight of m1 = m1g
force of friction of m2 = m m2g
Fnet = m1g - m m2g
Fnet = (m1 - m m2)g
since Fnet also = total mass of system * acceleration of the system,
Fnet=(m1 + m2) a
therefore,
(m1 - m m2)g = (m1 + m2) a
a=((m1 - m m2)g) / (m1 + m2)