Changes

The '''velocity''' of an object is a combination of both speed and direction: in formal terms, it is the rate of change of its [[displacement]] and direction of that change.  If the position of an object is some [[function]] of [[time]], then the velocity is the [[derivative]] of that function:

The '''velocity''' of an object is a combination of both speed and direction: in formal terms, it is the rate of change of its [[displacement]] and direction of that change.  If the position of an object is some [[function]] of [[time]], then the velocity is the [[derivative]] of that function:

:<math>v(t)={\mathrm{d}x \over \mathrm{d}t}</math>

:<math>\vec v(t)={\mathrm{d}\vec x \over \mathrm{d}t}</math>

where ''x'' is the position and ''v'' is the velocity. The velocity is a [[vector]], and its length or absolute value is called the ''[[speed]]''. The velocity has dimensions of length / time, and may thus be expressed in meters per seconds (in scientific usage), or miles per hour in more common usage.

where <math>\vec x</math> is the position and <math>\vec v</math> is the velocity. The velocity is a [[vector]], and its length or absolute value is called the ''[[speed]]''. The velocity has dimensions of length / time, and may thus be expressed in meters per seconds (in scientific usage), or miles per hour in more common usage.

For an object moving along a straight trajectory, if [[acceleration]] and velocity have the same sign, the object is gaining [[speed]].  If acceleration and velocity have different signs, the object is losing speed.

For an object moving along a straight trajectory, if [[acceleration]] and velocity have the same sign, the object is gaining [[speed]].  If acceleration and velocity have different signs, the object is losing speed.