Suppose a paticle travels from $A$ to $D$ inscribing a path like the one shown in the picture taking time $t$. My question is if I apply the equation of motion, which is $$s=ut + \frac 1 2at^2$$ where $u$ is the initial velocity and $v$ is the final velocity, will I get the length of path covered by the body(distance) or the length from $A$ to $D $(displacement) ? I know that in formulas, $s$ stands for displacement. But how can i get displacement which is $A$ to $D$ if I apply the time $t$ in the formulae which is the time taken by the body to inscribe the path $ABCD$ ?
(It is assumed the particle is traveling with uniform acceleration)