Relativistic velocity of a body under constant acceleration?

Question

Relativistic momentum, p = γ m_0 v, where γ is Lorentz factor 1/√(1 - v²/c²) and m_0 is rest mass of the body in question

Newton's 2nd, which still holds, is F= dp/dt

Assuming body starts at rest, change in momentum is still impulse thus if a force F acts on mass m_0 for t then γ m_0 v = F t

All correct so far?

Thus, for velocity as function of time (in the unaccelerated reference frame) I get

v(t) = (c F t)/√(m_0² c² + F² t²)

Is this correct?

Pearlsawme · Accepted Answer

Is Not correct.

The equation ( γ *mo v = Ft) is also not   correct. 

This is correct only for a small interval of time.
Hence you  have to wirte this as 
γ *mo v = F dt.
===========================
The correct form is  Fdt = d(mv) where m and  v  are variables and m depnends on v.

d(mv)  = mdv/dt + v dm/dt 

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Relativistic velocity of a body under constant acceleration?

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