VELOCITY AND ACCELERATION
For a moving body the distance traversed divided by the elapsed time is the speed of the body. If we take account of the direction of motion as well as the speed, we define the velocity of the body. A change in the state of motion or velocity, which is known as acceleration, can be due to a change in the speed or the direction of motion or both. Thus acceleration is measured as the rate of increase or decrease of a body's speed or as the rate at which its direction of motion changes. Since distance depends upon a frame of reference, then so also will velocity and acceleration.
An airplane's velocity, for example, is usually measured relative to the surface of the earth, say, 600 miles per hour. We could measure it relative to the sun, in which case the earth's rotational and orbital velocities would have to be added to that of the airplane. Any fixed point on the surface of the earth is continuously changing velocity-that is, accelerating-because of the spin of the earth on its axis of rotation and the revolution of the earth about the sun. What we really want to talk about in the case of the orbital motion of planets is the velocity at one single moment of time since an instant later the velocity will be different owing to acceleration. This concept of velocity is called instantaneous velocity.
QUANTITY OF MOTION: MOMENTUM
As you might guess, there is more to defining the motion of a body than simply finding a value for its velocity. For example, in the collision of two billiard balls moving with different velocities, it may appear that they simply exchange their states of motion so that the total quantity of motion is conserved and just redistributed between them. But in the case of two billiard balls of different masses moving with the same speed, the more massive one is able to transfer a greater qu'antity of motion in a collision than the small-mass ball can. Thus the concept of quantity of motion, or momentum, involves both the velocity and the mass of the body. To find momentum, we multiply the body's mass by its velocity.
It is not difficult to visualize philosophically the possibility that the total quantity of motion, or momentum, in the universe is a constant-that is, the total momentum of the universe is conserved although the interaction of various bodies in the universe with each other redistributes the momentum of individual bodies. This concept of conservation of momentum was first annunciated by the French natural philosopher Rene Descartes in his book, Principles of Philosophy, published in 1644.
