explain $["$A particle in rectilinear motion starts from rest and maintains the acceleration profile shown in Exhibit $3\mathrm{.}5.$ The displacement of the particle in the first $8$ seconds is:

a$.4$ m

b$.28$ m

c$.24$ m

d$.20$ m$"$

Accompanying figure $($Exhibit $3\mathrm{.}5)$ shows the acceleration aaa versus time ttt graph. The graph is piecewise:

From t$=0$t $=0$t$=0$ to t$=2$t $=2$t$=2$ seconds, a$=+4$m$/$s$2$a $=+4\backslash ,$ m$/$s$^2$a$=+4$m$/$s$2.$

From t$=2$t $=2$t$=2$ to t$=8$t $=8$t$=8$ seconds, a$=2$m$/$s$2$a $=-2\backslash ,$ m$/$s$^2$a$=2$m$/$s$2.$

The particle starts from rest, meaning its initial velocity v$0=0$ m$/$sv$\_0=0\backslash ,$ m$/$sv$0=0$m$/$s and initial displacement x$0=0$ mx$\_0=0\backslash ,$ mx$0=0$m$.]$ Explain what is needed to understand. the answer is d according to the book.