$1.2.20.$ The body starts moving from point $A$ and moves first equidistant for time $t_0$, then with the same modulo acceleration — equidistant. After what time from the beginning of the movement, the body will return to point $A$?
During the time $t_0$ the velocity of the body became equal to $v_0 = at_0$, and the coordinate $$x_0 = \frac{at_0^2}{2}$$ It takes time $t_1$ for the body to travel the distance $x_1$: $$-x_1 = v_0 t - \frac{at^2}{2}$$ Solving a quadratic equation: $$t_1^2 - 2t_0 t_1-t_0^2=0$$ We choose a positive root: $$t_1 = (1+\sqrt{2})t_0$$ Round trip time: $$T = t_0+t_1=(2+\sqrt{2})t_0$$
$$t =(2+\sqrt{2})t_0$$