4. Instantaneous velocity and speed

4. Instantaneous velocity and speed

• Velocity of particle at any instant of time or at any point of its path is called instantaneous velocity.
• Again consider the graph 5b and imagine second point Q being taken more and more closer to point P then calculate the average velocity over such short displacement and time interval.
• Instantaneous velocity can be defined as limiting value of average velocity when second point comes closer and closer to the first point.
• Limiting value of Δx/ Δt as Δt approaches zero is written as dx/dt, and is known as instantaneous velocity.Thus instantaneous velocity is
  
  
• As point Q approaches point P in figure 5a in this limit slope of the chord PQ becomes equal to the slope of tangent to the curve at point P.
• Thus we can say that instantaneous velocity at any point of a coordinate time graph is equal to the slope of the tangent to the graph at that point.
• Instantaneous speed or speed is the magnitude of the instantaneous velocity unlike the case of average velocity and average speed where average speed over an finite interval of time may be greater than or equal to average velocity.
• Unit of average velocity , average speed, instantaneous velocity and instantaneous speed is ms_-1 in SI system of units.
• Some other units of velocity are ft.s^-1 , cm.s^-1 .