The acceleration of a particle starting from rest varies with time according to the relation a=kt+c . Then the velocity v of the particle after a time t will be :
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a = dv/dt
integrate and find the expression for v.
the velocity changes from 0 to v as time changes from 0 to t.
I hope you understand the approach.
All the best!
integrate and find the expression for v.
the velocity changes from 0 to v as time changes from 0 to t.
I hope you understand the approach.
All the best!
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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)
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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