Question

At what velocity the kinetic energy of a body is equal to its rest mass energy.

Answer 1

The answer is 0.87c

Answer 2

consider the Einstein relativistic equation

E = Ek + Er

(Er is the rest mass energy)

So,  

mc² = Ek + m₀c²

Therefore kinetic energy of a particle is:

Ek = mc² - m₀c²

now applying the condition:

Ek = Er, and also relativistic mass m=m₀/√(1 - v²/c²)

m₀c²/√(1 - v²/c²) - m₀c² = m₀c²

m₀c²/√(1 - v²/c²) = 2m₀c²

1/√(1 - v²/c²) = 2

√(1 - v²/c²) = 1/2

1 - v²/c² = 1/4

v²/c² = 3/4

v = c√0.75

v = 259807.621 km/s

v=0.87c

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