Average Acceleration and Instantaneous Acceleration

A particle will accelerate, if its velocity is changing with time. Velocity change includes direction or magnitude or both.

Acceleration is the rate of change of velocity. Average acceleration is the change of velocity in a given time interval. Suppose a particle has a velocity V1 at time t1, and V2 at time t2, then

This means, average acceleration of the particle depends only on initial and final velocities. The velocities in between t1 and t2 will not bother in average acceleration.
Instantaneous acceleration is the acceleration at every instant of time.
Dimension of acceleration is LT^-2.
Consider a particle moves in X direction, and
  • If dx/dt  is positive, the direction of velocity is along the positive X – axis.
  • If dx/dt is negative, the direction of velocity is along negative X - axis.
  • If dv/dt  is positive, the direction of acceleration is along positive X-axis.
  • If dv/dt  is negetive, the direction of acceleration is along negative X-axis.
  • If velocity and acceleration both are positive or negative simultaneously, the speed increases.it means particle is accelerating.
  • If velocity and acceleration are opposite in sign, the speed will decrease, means particle is in decelerating (negative acceleration) mode.
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