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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

- Consider that acceleration a is some function of time such that

$a=f(t)$

this equation can also be written in terms of velocity i.e.

$a=\frac{dv}{dt}=f(t)$ …..1 - Now we integrate equation 1 as a function of time

$dv=f(t)dt$

$v=\int dv=\int f(t)dt +C$ ……2

here C is some constant of integration and can be calculated from the initial conditions. - Now we know that $v=\frac{dx}{dt}$ , using this in the solution of equation 2 we can easily find position of the particle.

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