A particle of mass m moves in xy plane such that its position vector, as a function of time, is given by `vec(r) =b(kt-sinkt)hati+b(kt+cos kt) hatj`. where b and k are positive constants. (a) Find the time `t_0` in the interval `o le t le (pi)/k` when the resultant force acting on the particle has zero power. (b) Find the work done by the resultant force acting on the particle in the interval `t_(o) le t le (pi)/4`

Answer

(a) `t_(0)=(pi)/(4K)`
(b) `W=((1+2sqrt(2))/2) mb^(2)k(