Question

The acceleration of a particle,starting from rest, varies with time according to relation a=kt+3 then the velocity v of the particle after a time will be?

Answer 1

Velocity of a particle is integral of its acceleretion. Therefore the velocity can be found by integrating the function with respect to time.
$a=kt+3 \\ \int{a \, dt= \int {kt} \, dt + \int {3} \, dt$
$v=k\int{t} \, dt + 3t \\ v= \frac{k t^{2} }{2} +3t+c$

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