How to solve problems involving time dependent acceleration





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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

  1. 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
  2. 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.
  3. 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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