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## Main Question or Discussion Point

Usually, equations of motion (with constant acceleration) are written in terms of values of position/velocity at time ##t=0##.

Take for example:

$$x = x_0 + v_0t + \frac{1}{2} a t^2$$

Where ##x_0## and ##v_0## are the values (at ##t=0##) of position and velocity respectively.

What if we're given position at some other time ##t=t_0##, instead of ##t=0##, and we're asked to find ##x## as a function of time?

What I do is I find a more general form of the equation I wrote above as follows:

$$\int_{x_0}^x dx' = \int_{t_0}^t v(t') dt'$$

Where ##x_0## now represents position at time ##t=t_0##.

Another way would be to eliminate the variable ##x(0)##

Is there any alternative approach?

Take for example:

$$x = x_0 + v_0t + \frac{1}{2} a t^2$$

Where ##x_0## and ##v_0## are the values (at ##t=0##) of position and velocity respectively.

What if we're given position at some other time ##t=t_0##, instead of ##t=0##, and we're asked to find ##x## as a function of time?

What I do is I find a more general form of the equation I wrote above as follows:

$$\int_{x_0}^x dx' = \int_{t_0}^t v(t') dt'$$

Where ##x_0## now represents position at time ##t=t_0##.

Another way would be to eliminate the variable ##x(0)##

Is there any alternative approach?

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