If the initial position of a particle is vec$(r)(0)=($:$0,0,0$:$),$ the initial velocity is vec$(v)(0)=($:$0,0,2$:$),$ and the acceleration is given by vec$(a)(t)=costvec(i)sintvec(j)$ vec$(k),$ where $t$ is measured in seconds, find the position of the particle after $5$ seconds.

Select one:

a$.$ vec$(r)(5)=(1-cos5)vec(i)(5-sin5)vec(j)\frac{45}{2}$vec$(k)$

b$.$ vec$(r)(5)=(1-cos5)vec(i)-sin5$vec$(j)\frac{25}{2}$vec$(k)$

c$.$ vec$(r)(5)=-cos5$vec$(i)-sin5$vec$(j)\frac{25}{2}$vec$(k)$

d$.$ vec$(r)(5)=-cos5$vec$(i)(5-sin5)vec(j)\frac{45}{2}$vec$(k)$

e$.$ None of the above