Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows:
A body remains at rest, or in motion at a constant speed in a straight line, except insofar as it is acted upon by a force.
At any instant of time, the net force on a body is equal to the body's acceleration multiplied by its mass or, equivalently, the rate at which the body's momentum is changing with time.
If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.
The three laws of motion were first stated by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), originally published in 1687. Newton used them to investigate and explain the motion of many physical objects and systems. In the time since Newton, new insights, especially around the concept of energy, built the field of classical mechanics on his foundations. Limitations to Newton's laws have also been discovered; new theories are necessary when objects move at very high speeds (special relativity), are very massive (general relativity), or are very small (quantum mechanics).
Given is the diagram shown in the context:
My solution:
However, the correct solution is
I am confused with the direction and signs of the system. How would I derive the solution?
Thank you for your help.