Formulae: $v_x=d\frac{x}{d}t$;$,a_x=d\frac{v_x}{d}t$ or $a_x=v_{x}d\frac{v_x}{d}x$;$v=d\frac{s_{\text{I}}}{d}t$;$a_n=\frac{v^2}{}$;$,a_t=d\frac{v}{d}t$;

$x_B=x_A+x_{\frac{B}{A}}$;$,{\displaystyle \underset{i}{\overset{?}{}}}{F}_{}=m{a}_x$;$,F_{fk}={}_{k}N$;$,F_{fs}{}_{s}N$;$,F_{\text{e}\text{l}\text{x}}=-kx$;$,U_{1-2}={\displaystyle \underset{s1}{\overset{s2}{}}}$Fcos$ds$;

$T_l+{\displaystyle \underset{?}{\overset{?}{}}}{U}_{l-2}=T_2$;$m(v_x{)}_1+{\displaystyle \underset{t1}{\overset{t2}{}}}{F}_{x}dt=m(v_x{)}_2$;${\displaystyle \underset{?}{\overset{?}{}}}{m}_i(v_{ix}{)}_1+{\displaystyle \underset{t1}{\overset{t2}{}}}{F}_{ix}dt={\displaystyle \underset{?}{\overset{?}{}}}{m}_i(v_{ix}{)}_2$;

The force $F$ acting on the crate A varies as shown in the graph.

The crate is on a smooth surface. The mass of the crate is $m=400kg.$ The crate is at rest at $t=0.$

Answer the questions:

What is the impulse of the force $F$ during the first $5$ seconds? $(3$ points$)$

A