(N/A) The kinetic energy $(K_{max})$ of a photoelectron is given by Einstein's photoelectric equation: $K_{max} = h\nu - \Phi_0$,where $h\nu$ is the energy of the incident photon and $\Phi_0$ is the work function of the metal surface.
$1$. By definition,kinetic energy is the energy possessed by an object due to its motion,which is given by the formula $K = \frac{1}{2}mv^2$. Since mass $(m)$ is always positive and the square of velocity $(v^2)$ is always non-negative,kinetic energy can never be negative.
$2$. Physically,if the incident photon energy $(h\nu)$ is less than the work function $(\Phi_0)$,the photon does not have enough energy to eject an electron from the metal surface at all. In this case,no photoelectric emission occurs,and the kinetic energy is not defined as negative; rather,the process simply does not take place.