section_path: Description of objects and their motion/Kinematics/Velocity and speed
section_name: Velocity and speed
paragraph_text: Velocity and speed
  
  The velocity, or the rate of change of displacement with time, is defined as the derivative of the position with respect to time:
  
  In classical mechanics, velocities are directly additive and subtractive. For example, if one car travels east at 60 km/h and passes another car traveling in the same direction at 50 km/h, the slower car perceives the faster car as traveling east at 60 − 50 = 10 km/h. However, from the perspective of the faster car, the slower car is moving 10 km/h to the west, often denoted as −10 km/h where the sign implies opposite direction. Velocities are directly additive as vector quantities; they must be dealt with using vector analysis.
  
  Mathematically, if the velocity of the first object in the previous discussion is denoted by the vector u = u d and the velocity of the second object by the vector v = v e, where u is the speed of the first object, v is the speed of the second object, and d and e are unit vectors in the directions of motion of each object respectively, then the velocity of the first object as seen by the second object is:
  
  Similarly, the first object sees the velocity of the second object as:
  
  When both objects are moving in the same direction, this equation can be simplified to:
  
  Or, by ignoring direction, the difference can be given in terms of speed only: