To mathematically derive that acceleration is constant using the equation F = ma, we need to make certain assumptions and simplifications. Here's a step-by-step explanation:
Assume that the mass of the object remains constant throughout the motion.
Start with Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration: F = ma.
Suppose the object is experiencing a constant net force, F, in a particular direction.
If the force is constant and the mass is constant, then the acceleration, a, must also be constant. This is because the equation F = ma implies that the acceleration is directly proportional to the force acting on the object. If the force remains constant, the acceleration will also remain constant.
Therefore, in this specific scenario where the net force acting on the object is constant, we can conclude that the acceleration is constant as well.
It's important to note that this derivation assumes a simplified scenario where the net force is constant and the mass remains constant. In real-world situations, forces acting on objects can vary, leading to changes in acceleration.