Suppose a particle of mass m has position given by r(0) =< 1,0,0 > , and velocity given by v(0)0,1,-1 > at time t = 0. also, assume that for every time t 20 the particle experiences only the force given by the vector function f(t) = m < -cos(t), 0, sin(t) > . disregard units in this problem a) use newton's second law, f(t) = ma(t) (where a(t) is the acceleration vector of the particle at time t) in order to show that r(t) =< cost, t,-sin t > gives the particle's position at time t, for t 2 0. show all the necessary work to find this position vector function, do not simply check that it is correct b) sketch the particle's path for t 2 0 c) determine the curvature of the particle's path at time t d) assume a second particle is also present, and has a position given by the vector equation r2(t)sin(t)-1,n-t, cos(t) -1> , for t 2 0. determine at which times (if any) the particles collide. determine at which points in space (if any) the paths of the particles intersect