Newton's second law of motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, it can be expressed as:
F = ma
where: F is the net force acting on the object, m is the mass of the object, and a is the acceleration produced by the net force.
If a body is moving with a constant velocity, it means that its acceleration is zero. In this case, the equation F = ma simplifies to:
0 = m * 0
Since any number multiplied by zero is zero, we can see that the net force acting on the object is zero. In other words, when a body is moving with a constant velocity, the net force acting on it is balanced or canceled out.
This can be understood intuitively by considering that if the net force is not zero, it would cause an acceleration, either speeding up or slowing down the object. But if the object is moving at a constant velocity, it means the forces acting on it are in equilibrium, and the net force must be zero to maintain that state of motion.
Therefore, a body moving with a constant velocity has a zero resultant force because the forces acting on it are balanced, satisfying Newton's second law of motion.