You bet it is! The condition is that v is much less than c.
The rest energy of a thing is E = mc2.
i recall seeing this proof when reading asimov.
i found this was a different source.
The total energy of a thing is gamma×mc2.
The kinetic energy is the difference of these, KE = (gamma – 1)mc2.
Recall that gamma = (1 – (v/c)2)-1/2. Expanding this in Maclaurin series it’s:
gamma = 1 + 1/2 (v/c)2 – 3/8 (v/c)4 + …
So KE = (1/2 (v/c)2 – 3/8 (v/c)4 + … )mc2
If v is much less than c, we can approximate this with just the first term, so
KE is approximately 1/2 (v/c)2 mc2 = 1/2 mv2