Can kinetic energy be added linearly?

[kbar1]

According to special relativity, velocity cannot be added to another velocity linearly. But I was thinking, what about kinetic energy? K.E. = mv²/2. As velocity increases, the object's mass also increases. The way I see it, the increase in mass "compensates" for the less-than-expected increase in velocity (as predicted by classical mechanics). So am I right in saying, kinetic energy can be added linearly?

Does what I said above agree with relativistic K.E. equation: K.E. = ($\gamma$-1)mc² ?

 

[PeterDonis]

The way I see it, the increase in mass "compensates" for the less-than-expected increase in velocity (as predicted by classical mechanics).

Have you actually checked the math?

Does what I said above agree with relativistic K.E. equation: K.E. = ($\gamma$-1)mc² ?

This is the correct equation; so have you checked to see what happens when you transform between frames?