The most complicated part of physics is not memorizing the many equations at your disposal, but being able to manipulate and mix these equations to obtain the correct answer. Finding power when given only velocity and mass may seem daunting, but become quite simple once you know the right equations.
How to Mix Equations

Mixing equations is a crucial skill in physics. Even if you've forgotten the equation for one particular variable, you can usually put together a few other equations and find the answer you need. The power equation contains only one small exception to the rule.
The Equation for Power

The basic equation for power is P=W/t where "W" = work and "t" = time. The one limitation to finding power using mass and velocity is that you must also have time. Time is a very commonly given variable however, if you are working in a classroom setting.
The Other Equation Needed

The goal now becomes finding work given only mass and velocity. The equation required to do this will be the equation for work as it relates to kinetic energy: W = ?KE = 1/2m(vf  vi)^2. In this equation m is mass, vf is final velocity, and vi is initial velocity.
Putting It Together

Now that we have an equation for work that consists entirely of mass and velocity, all that's left is to replace the "W" in the equation for power from Section 1, with the equation we just found in Section 3. This leaves us with the equation P = [1/2m(vfvi)^2] / t.