A particle is acted by three forces as shown in the figure....

A particle is acted by three forces as shown in the figure. Then:
(a) the resultant force on the particle may or may not be zero
(b) the particle must be in rest
(c) the direction of acceleration is in indeterminate form
(d) the particle moves with variable velocity

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Key Concepts

Newton's Second Law of Motion

Newton's second law states that the acceleration of a particle is directly proportional to the net force acting on it and inversely proportional to its mass. This law establishes that the direction and magnitude of acceleration are dictated by the net unbalanced force, which is central to analyzing particle dynamics under various force configurations.

Motion Under Varying Forces

When a particle is subjected to forces that are not balanced, the resulting net force causes acceleration, leading to changes in the particle's velocity over time. This concept highlights that variable net forces produce variable acceleration and, consequently, non-uniform motion.

Vector Addition of Forces

Forces are vectors, meaning they have magnitude and direction, and the net force acting on a particle is the vector sum of all individual forces. This concept is fundamental in determining whether a system is in equilibrium or if there is a resultant force causing acceleration.

Equilibrium

Equilibrium occurs when the sum of all forces acting on a particle is zero. In equilibrium, there is no net force, and therefore, no acceleration according to Newton's first law. This concept helps in understanding under what conditions a particle might remain at rest or move with constant velocity.

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