Why force is equals to product of mass and acceleration?

Answer 1

It goes to the heart of Newtons laws: an object in motion will tend to stay in motion unless an outside force is applied. Force is just a measurement of how much an object 'wants' to stay in motion.

The total energy (velocity and mass) of an object measures the resistance to change an object has. Given a perfect system two cars of the same mass moving at the same speed heading towards each other will collide and stop - they cancel each other out. Force is a way of saying what energy it will take to cancel the motion of an object out. You can use a slower, heavier object to counter the motion OR a faster, lighter object to cancel the motion.

F=MV and not F=M+V is because

the acceleration is to the whole object (applied all over)

you can't add a scalar and a vector (mass is the scalar.) You can however multiply a vector by a scalar.

Answer 2

Force is equal to the product of mass and acceleration because it represents how an object's motion changes when a force is applied. Acceleration is directly proportional to the force applied to an object (Newton's second law), and mass represents an object's resistance to changes in motion. Therefore, multiplying mass by acceleration gives us the force needed to accelerate the object.