Derive an expression for average velocity and instantaneous velocity for the motion of an object in x-y plane.

Asked by Tinuomrajankar | 6th Sep, 2021, 10:26: AM

Expert Answer:

  • Acceleration is defined as the rate of change in velocity with time.
    Acceleration = Change in velocity/ Time taken 
    Average acceleration = Total change in velocity/ Total time taken 
    Thus, average acceleration, 
    a space equals stack space l i m with capital delta t rightwards arrow 0 below fraction numerator capital delta v over denominator capital delta t end fraction space equals space fraction numerator d v over denominator d t end fraction
    Instantaneous velocity: -It is the velocity of the particle at a given instant. The direction of instantaneous velocity is

along the tangent drawn to the curve describing the path at that instant if the body undergoes

curvilinear motion. 

    v space equals stack space l i m with capital delta t rightwards arrow 0 below v with bar on top space equals space stack space l i m with capital delta t rightwards arrow 0 below fraction numerator capital delta x over denominator capital delta t end fraction space equals space fraction numerator d x over denominator d t end fraction

Answered by Shiwani Sawant | 6th Sep, 2021, 10:53: AM