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Assuming the force is in the direction of the velocity, the relativistic form of $F=ma$ is $$F=\gamma^3 m_o a.$$ The term relativistic mass has become outdated recently, but it refers to the quantity $M=\gamma m_o$, where $m_o$ is the rest mass. While not necessary, we can keep this product explicit in the following rearrangement: a=\frac{F}{\gamma^2 ...

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$\Sigma F = ma$. Therefore, if a net force $n$ is applied to an object, it will accelerate. You are correct that the acceleration will decrease, since $m$ increases, but it will never quite reach zero.

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