To my (very performance limited) knowledge...
For Performance A Aircraft ( for those unfamiliar, simply said your airliner)
V2= 1.2 Vs= 1.1 Vmca~(approximates) Vx
V2+15~(approximates) Vy
Where Vx is the Best ANGLE of climb
Vy is the Best RATE of climb
Vs is the Stall Speed for given flaps
Vmca is the Speed Minimum Control Ground ( min. rudder control speed)
We want to fly on jets on Vy because it gives us the least time to reach a certain altitude, thus more economical and above all, the safest thing to do in case of engine failure (think of your EFFRA, Engine Failure Flaps Retraction Altitude). If we would fly V2, this would give us a very slight margin to correct in case of engine failure, (10%),although with both engines working, V2 will protect us for all normal manoeuvres ( standard rate turns).
What Old Smokey wrote about which speeds to choose when the engine says kabooum is a very good thing by the way! thanx for that, never actually thought about it...