To determine the rate at which kinetic energy is imparted, we must find the Power ($P$) delivered by the engine. Power is defined as the rate of change of energy over time ($P = \frac{dE}{dt}$) .

1. Kinetic Energy (KE): The kinetic energy of a mass $M$ moving with velocity $v$ is given by $KE = \frac{1}{2}Mv^2$ .
2. Rate of Kinetic Energy: For a continuous jet where velocity $v$ is constant, the rate of change of kinetic energy is $P = \frac{d(KE)}{dt} = \frac{1}{2}v^2 \frac{dM}{dt}$.
3. Mass Flow Rate ($\frac{dM}{dt}$): We are given the mass per unit length $m = \frac{dM}{dl}$. In a small interval of time $dt$, the length of the water column leaving the hose is $dl = v dt$. Therefore, the mass flow rate is: $\frac{dM}{dt} = \frac{dM}{dl} \cdot \frac{dl}{dt} = m \cdot v$
4. Final Calculation: Substituting the mass flow rate back into the power equation: $P = \frac{1}{2}v^2 (mv) = \frac{1}{2}mv^3$

Thus, the rate at which kinetic energy is imparted to the water is $\frac{1}{2}mv^3$.