This is easiest to solve by recognising that the nurse is doing work on the mass which results in a transfer of energy into kinetic energy
#FtimesS= 1/2mv^2#
Rearranging
#F=(mv^2)/(2S)#
Substituting in:
#F=((3times10^-3) times (1.4^2))/(2 times 0.034)=0.086N#