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## Homework Statement

Suppose a constant force F acts on a particle of mass m initially at rest.

(a) Integrate the formula for acceleration [tex]\vec{a} = \frac{\vec F}{\gamma m} - \frac{\vec v}{\gamma mc^2}(\vec F \cdot \vec v)[/tex] where [itex]\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}[/itex] to show that the speed of the particle after time t is given by [tex]\frac{v}{c} = \frac{(F/m)t}{\sqrt{(F/m)^2t^2+c^2}}[/tex]

## Homework Equations

Given above

## The Attempt at a Solution

I have taken Calc. 1-3, differential equations, and linear algebra, and yet I still do not know how to integrate the formula for the acceleration [itex]\vec a[/itex] shown above. I don't think that I've ever integrated vectors, and especially not dot products; so I have no idea where to even start. This is part of a special relativity section for an bachelor's level Astrophysics course. Any help would be greatly appreciated!

Thanks!