Motion in a plane

4. Average and instantaneous acceleration

  • Suppose a particle moves from point P to point Q in x-y plane as shown below in the figure

    Average accleration vector representation

  • Suppose v1 is the velocity of the particle at point P and v2 is the velocity of particle at point Q
  • Average acceleration is the change in velocity of particle from v1 to v2 in time interval Δt as particle moves from point P to Q. Thus average acceleration is

    Average accelaration is the vector quantity having direction same as that of Δv.
  • Again if point Q aproaches point P, then limiting value of average acceleration as time aproaches zero defines instantaneous acceleration or simply the acceleration of particle at that point. Ths, instantaneous acceleration is

  • Figure below shows instantaneous acceleration a at point P.

    instantaneous acceleration at a point

  • Instantaneous acceleration does not have same direction as that of velocity vector instead it must lie on the concave side of the curved surface.
  • Thus velocity and acceleration vectors may have any angle between 0 to 180 degree between them.

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