An engine pump ejects a liquid of density $\rho$ through a pipe of cross-sectional area $A$. If the velocity of the liquid coming out of the pipe is $v$,find the rate at which kinetic energy is imparted to the liquid.

• A
  $\frac{1}{2}A\rho v^3$
• B
  $\frac{1}{2}A\rho v^2$
• C
  $\frac{1}{2}A\rho v$
• D
  $A\rho v$