The SI unit of acceleration is m/s2, or more appropriately, meters per second per second. It is described mathematically as v/t, which is change of velocity over change in time. It describes the rate at which velocity changes over time. On the other hand motion is the change of position of an object with regards to a particular frame of reference. According to Newton, a body’s motion does not change unless a force acts on it. A body can either be at rest, or in motion when an external force acts upon it. Motion may be described as the difference between an object’s kinentic energy and potential energy. As one form of energy goes increases, the other necessarily decreases. According to Newton the laws of motion are 1) if the forces on an object are balanced then the object will continue to move as it is, 2) if the forces are unbalanced then an object will change its motion, and 3) every action has an equal and opposite reaction.
An example of motion would be simply giving the absolute value of the distance moved by an object in relation to a previous position. A baseball bat hitting a ball is an example of motion, the force hitting the ball changes the baseballs motion, and there is an equal force from the ball hitting the bat. Acceleration though, as described above, is the change in velocity over time – a car accelerating from 0-60 mph over a period of time is a good example.
The evolution of acceleration was key to Newtonian understanding because of the simple equation F=MA, that is Force = Mass x Acceleration. With this equation, it became possible to predict the forces that would be applied to an object, the rate at which they would change direction, and it allowed for him to predict the eventual location of an object with a great deal of certainty.
Holzner, Steven. Physics Essentials for Dummies. New York: For Dummes,
Kuhn, Karl F. Basic Physics: A Self-Teaching Guide (2nd ed). New York: Wiley, 1996.