[Maximum mark: 13]A particle P moves in a straight line such that after time t seconds, its velocity, vinms-1,is given byv=e-3tsin6t, where Pt,Ps(t)t=0,s(0)=0PPP0ms-2PPt1,t2,t3v1,v2,v3tan6t=2v2v1=v3v2=-e-2t1 and the respective velocities are v1,v2,v3.(d) Show that, at these times, tan6t=2.(e) Hence show that v2v1=v3v2=-e-2.0.(a) Find the times when P comes to instantaneous rest.At time t,P has displacement s(t); at time t=0,s(0)=0.(b) Find the maximum displacement ofP,in metres, from its initialposition.(c) Find the total distance travelled byPin the first 1.5 secondsof its motion.At successive times when the acceleration ofPis0ms-2, the velocities ofPform a geometric sequence. The acceleration ofPis zero at times t1,t2,t3where t1 and the respective velocities are v1,v2,v3.(d) Show that, at these times, tan6t=2.(e) Hence show that v2v1=v3v2=-e-2.