Question

Acceleration of a particle discharge from this varies with time according to the relation

Answer 1

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Acceleration of a particle is the time derivate of its velocity.

Hence, the velocity of the particle at any time instant would be the integral of its acceleration. 

Velocity at time t = ∫ acceleration from time 0 to time t

Velocity at time t= ∫(kt+ c)dt. (from limits 0 to t)

                          =k ∫tdt+ c∫dt (from limits 0 to t)

Putting in the limits, 

                          =kt²/2 +ct

hence the velocity of the particle at time t is given by the expression (kt²/2 + ct)(assumed k and c to be constants) .

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