Sorry if this question is dumb, and I know is physics 101, but I'm not that good with physics.
I'm writing an iPhone program that by collecting the acceleration data of the device tries to replicate the motion of the device in an virtual environment.
To simplify things, let's consider just one axis.
If the device is at position 0 with acceleration 0 and speed 0, if it receives an acceleration of 1.25G, what it will be it's position after 1.22 seconds, considering that the acceleration will last for the whole 1.22 seconds?
Answer
We are looking for the position, say $s$, of the object at a certain time $t$. Given initial conditions $t_0$ (initial time), $v_0$ (velocity at $t_0$), $s_0$ (position at $t_0$) and a constant acceleration $a$ during a time interval $t - t_0$.
We use the following equation to determine the position $s$ at time $t$:
$$s = s_0 + v_0(t-t0) + \frac {1}{2}a(t-t_0)^2$$
(This page would be helpful if you need more.)
Hope this helps!
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