Newton gave a relationship between force, mass and acceleration and he called it a Second Law of Motion. From the animations can be noted that the acceleration that the body receives is directly proportional to the size of the force (in the direction of the force) and inversely proportional to the mass of the body.

Or the most common form of the Second Newton's law:

Source: https://road2animate.wordpress.com/2010/06/26/laws-of-motion-useful-knowledge-for-animators/

Example: Pushing a cart across a frictionless surface. If we want to increase the speed of the cart's movement (increase in acceleration), we would push harder (increase in force). If the cart was replaced with a car (increase in mass), we would have to push even harder than the previous time (increase in force) to speed it up at the same rate as the cart.