Two dimensional motion
Galileo was the first to realize that a moving body can have several separate motions, which are independent of each other. His thinking provides a foundation for Newton's treatment of acceleration and force.
A body moving at constant velocity can be described by a sum of velocities in two directions, typically x and y co-ordinates.
The path of a projectile may combine constant speed in the horizontal direction with acceleration due to gravity in the vertical direction. This independence of vertical and horizontal motions is counter-intuitive, and only careful teaching combined with demonstration experiments will convince students.
Accelerations have the same additive properties. They too are vectors that can be added by constructing a parallelogram. Forces too are vectors and obey the same addition rule. In other words: when several forces act on a body, each produces its own effect on motion. One force does not interfere with the motion produced by another force.