Difference between revisions of "Velocity"

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m (correction)
(speed = rate of change in position - velocity is rate of change in displacement)
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The '''velocity''' of an object is the rate of change of its [[position]]. If the position of an object is some [[function]] of [[time]], then the velocity is the [[derivative]] of that function:
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The '''velocity''' of an object is the rate of change of its [[displacement]]. 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>v(t)={\mathrm{d}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 meter per second (in scientific usage). In daily life, miles per hour and kilometers per hour are more common units.
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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).
  
 
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.

Revision as of 16:37, 12 November 2007

The velocity of an object is the rate of change of its displacement. If the position of an object is some function of time, then the velocity is the derivative of that function:

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).

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.

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