Newton's Second Law of Motion.
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Newton's Second law states that the rate of change of momentum of an object is directly proportional to the unbalanced force in the direction of force.
Therefore, F is directly proportional to ma.
Force applied by Newton causes the rock to move only slightly.
Why don't you try to move the rock?
Force applied by the horse causes the rock to move a greater distance.
Newton applies less force, less acceleration is produced.
Horse applies more force, more acceleration is produced.
Hence, force is proportional to acceleration.
Mass of Newton is less, therefore applied force is less.
Mass of horse is more, therefore applied force is more.
Therefore, force is directly proportional to mass.
Force is directly proportional to mass.
Force is directly proportional to acceleration.
Hence, force is directly proportional to the product of mass and acceleration.