How to solve problems involving time dependent acceleration

Here i tried to sum up the steps to solve problems involving time dependent acceleration. We can easily calculate the position of the particle/object
(1) Consider that acceleration a is some function of time such that
this equation can also be written in terms of velocity i.e.
a=dv/dt=f(t)                                        .....1
(2) Now we integrate equation 1 as a function of time
v=∫dv=∫f(t)dt + C                ......2
here C is some constant of integration and can be calculated from the initial conditions.
(3) Now we know that v=dx/dt , using this in the solution of equation 2 we can easily find position of the particle.

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