Does Special Relativity Affect the Work Needed to Accelerate a Particle?

[matpo39]

ok i have a question from mastering physics i thought i was doing it right but it gives me an incorrect answer.

How much work must be done on a particle with a mass of m to accelerate it from rest to a speed of v_1? (Express the answer in terms of mc^2.)

I figured that this would just be the kenetic energy which is givin by

K= mc^2/(sqrt(1-(v/c)^2) - mc^2

so i factored out an mc^2 and was left with

work= (1/sqrt(1-(v/c)^2) -1)*mc^2

but mastering physics says that the answer does not depend on c.
i don't see how this is possible

thanks for the help

 

[vincentchan]

Express the answer in terms of mc^2. the answer is $$\gamma -1$$

 

[matpo39]

yes, that is my problem, the definition of gamma is 1/(sqrt(1-9V/c)^c)
so gamma itself contains a c and i don't think mastering physics will except the variable expression gamma as part of the answer because it is no where to be found in the problem.