Yes, the kinetic energy of the particle can be determined if the value of linear momentum is known.The kinetic energy is calculated using the formula:K.E=21​mv2=2mp2​where, p is the linear momemtum having value mv.But linear momentum cannot be determined even if the kinetic energy is known because linear momentum is a vector quantity, whereas kinetic energy is a scalar quantity. Thus, the direction of the linear momentum remains unknown, however its magnitude can be calculated.