Integration of motion equation

1. Jul 28, 2011

abedoui

Hi , I am trying to integrate this equation :
X"(t) = F(t) - 1 where X'(0) = X(0)= 0
F(t) force of a rocket , 0<t<T

solution they got : X(T) = [integral 0 to T of { (T-t)F(t)d(t) } ] - [square of T ] / 2

2. Jul 29, 2011

CompuChip

If X''(t_0) = F(t_0) - 1, then
$$X'(t_1) = \int_0^{t_1} X''(t_0) \, dt_0$$
and
$$X(t_2) = \int_0^{t_2} X'(t_1) \, dt_1 = \int_0^{t_2} \int_0^{t_1} X'(t_0) \, dt_0 \, dt_1$$.

3. Jul 29, 2011