The first of Sir Isaac Newton's Three Laws of Motion, which form the basis of classical mechanics, states that an object at rest or in a state of uniform motion will remain that way indefinitely in the absence of an external force. In other words, a force is that which causes a change in velocity, or acceleration. The amount of acceleration produced on a object by a given force is determined by the object's mass.
Force and Velocity Are Directional
When physicists speak about an object's velocity, they are talking not only about the object's speed but also about the direction in which it's moving. Similarly, force has a directional component as well as a quantitative one -- a force directly opposing an object's velocity has a different effect on the object than a force acting at right angles to its motion. In mathematical terms, force, velocity and acceleration -- which is the rate of change of velocity produced by a force -- are "vector" quantities, which is a term that implies their directional component.
Forces Acting on an Airplane
The easiest way to understand how a force alters an object's velocity is to imagine that force acting in the same direction as the velocity. For example, the jet engines on an airplane provide a force that acts in the direction of the airplane's motion, giving it a positive acceleration and making it go faster. Air friction, on the other hand, directly opposes the airplane's motion and decelerates it; if the engines stop working, the airplane will fall out of the sky. But when the force of the engine and the upward thrust of air pressure on the aerodynamically designed wings balance the force of friction and other decelerating forces, including gravity, the airplane flies at a constant velocity toward its destination.
The Force of Gravitation
The gravitational attraction that the sun exerts on the Earth is an example of a force with an important directional component. Because the gravitational force acts at right angles to the Earth's motion, it doesn't change the speed at which the planet travels, but it constantly changes the direction. As a result, the Earth moves in a nearly circular orbit. The Earth's speed may be relatively constant, but its velocity is always changing as a result of the force of gravitation that is always pulling it toward the sun. The same gravitational force keeps satellites in orbit around the Earth.
The mathematical relationship between force (F) exerted on an object and its acceleration (a) is F = m•a, where "m" is the mass of the object. The unit for force in the metric system is the newton, which is named after Isaac Newton, the English physicist who formulated the relationship. In the real world, there are usually several forces acting on a body, each with a directional component. These forces may be mechanical, gravitational, electrical or magnetic in nature. To predict the motion of the object, it's often useful to draw a free-body diagram, which is a graphical representation of these forces that depicts the magnitude and direction of each.