Please show work on paper If f is a vector-valued function defined by f|t|=(:sinsin|t|,e-x:), find f|t|.Let f be the vector-valued function defined by f|t|=(:4tt4,-3t2-t:). Find f|3:||.For time t>0, the position of a particle moving in the xy-plane is given by the vector (e2,1e2? What is the velocity vector for the particle at time t=1?A particle moves in the xy-plane so that at any time t its coordinates are x=t2-t and y=2t3-3t3. Find its acceleration vector at t=2.A particle moves in the xy-plane with position given by {:x|t|,y(t)