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 the object's [[displacement]], and the 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>\vec v(t)={\mathrm{d}\vec x \over \mathrm{d}t}</math>

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

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.

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 its [[acceleration]] and velocity have the same direction, the object is gaining [[speed]].  If its acceleration and velocity have opposite directions, the object is losing speed.

If velocity is [[zero]], [[acceleration]] is not necessarily zero. If acceleration is zero, velocity is constant, but not necessarily zero.

Even if an object's velocity is [[zero]], its [[acceleration]] is not necessarily zero. For example, consider a baseball thrown straight up into the air. At the top of its trajectory, it is momentarily motionless (and thus has zero velocity) even though its acceleration is not zero (it is still being pulled downwards by gravity).

 

If an object's acceleration is zero, its velocity is constant, but not necessarily zero.

[[Category:Physics]]

[[Category:Physics]]

[[Category:Mechanics]]

[[Category:Mechanics]]