A particle moves along the $y-$axis so that its velocity at any time $t0$ is $v(t)=tcost.$ At time $t=0,$ the position of the particle is $y=3.$

a$)$ For what values of $t,0t5,$ is the particle moving upward?

b$)$ Write an expression for the acceleration of this particle in terms of $t.$

c$)$ Write an expression for the position, $y(t),$ of the particle.

d$)$ For $t>0,$ find the position of the particle the first time the particle's velocity is $0.$