Joules required to accelerate 1kg of mass

[ally1h]

Homework Statement

how many joules of energy are required to accelerate 1 kg of mass from rest to a velocity of 0.866c?

I tried the relativistic kinetic energy equation, but I feel like it's totally incorrect.

Homework Equations

KE = [(m0c^2) / √(1-v^2/c^2)] - m0c^2
E = KE + m0c^2

The Attempt at a Solution

KE = [(1 kg*m^2/s^2) / √(1 - (0.866c)^2)] - (1 kg*m^2/s^2)
KE = [(1 kg*m^2/s^2) / √(1 -0.75 m^2/s^2) - (1 kg*m^2/s^2)
KE = [(1 kg*m^2/s^2) / (0.5 m/s)] - (1 kg*m^2/s^2)
KE = 2 kg*m/s - 1 kg*m^2/s^2
KE = 1 J

 

[tiny-tim]

Hi ally1h!

how many joules of energy are required to accelerate 1 kg of mass from rest to a velocity of 0.866c?
…
KE = [(m0c^2) / √(1-v^2/c^2)] - m0c^2
E = KE + m0c^2
…
KE = 1 J

one joule!

Hint: what happened to your c²?