A particle of mass m is subjected to a net force F(t) given by F(t)=Fo(1-t/T)i; that is, F(t) equals Fo at t = 0 and decreases linearly to zero in time T. The particle passes the origin x = 0 with velocity voi. Show that at the instant t = T that F(t) vanishes, the speed v and distance x traveled are given by v(T) = vo + aoT/2, and x(T) = voT + aoT^2/3, where ao = Fo/m is the initial acceleration.