The position of a particle of mass m moving freely in two dimensions in an inertial cartesian coordi- nate system is given by (xy). write down the particle's kinetic energy t(xý) and the equations of mo- tion. generalized coordinates qi (x, y, t) and q2 (x, y, r) are defined by 4-xcosot + ysinar -xsin cot + ycosot where co is a constant. write down the inverse transformations, x(1.42,t) and y(g1.9) and hence find an expression for t(4,.iz) in the new coordinates. obtain the equations of motion in the new coordi- nates (including the generalized forces qi and q2). identify the extra terms that appear, in terms of so- called "fictitious forces".