Pls write it out, show all work. Please do 5 ,6 ,7

5) r(t) = (sin 2t, cos 6t) is the position vector of a particle moving in the plane at time t. Find a) The velocity vector Vlo/ = (2cos)6,-6 sialbe) b) The acceleration vector alt/ =(-4sin (26), -36 105(60]) c) The speed at the given time t = - Speed : 12 X r (t ) = ( sin 26, cor6+) v ( 6 ) = 2 ear 20 1+ bras 1651 ; alt) = - 45in (26)i - 36cor(Gol/j speed : 1 ( 2 cus 26) 2 + ( Grin (6all? V 4 cas?2 6 + 36 ri" chel 54 ( case ) + 9 sin? (6(311 = 12 6) The velocity v(t) of a particle moving in the plane is given along with the position of the particle at time t=0. Find the position of the particle at time t=3 and v(t) =