Special Case: Constant Acceleration
However, for the continuous case, we get:
x(t) - xo = t=0?t vx(t) dt , which becomes
x(t) - xo = t=0?t (vxo + axt) dt , or
x(t) = xo + vxo *t + (1/2)*ax*t2 .
Note: In going backwards, as in the discrete case, we do need to know the initial conditions. In this case, the initial conditions are xo and vxo .