# Low-Speed Lorentzian Physics

Consider a particle with rest-mass $$(m_0 = \SI{1}{\kilo\gram})$$ and velocity $$v$$. Suppose we're in an alternate universe in which the "cosmic speed limit" is only $$\SI[per-mode=symbol]{10}{\meter\per\second}$$, and that the particle's mass varies with its velocity in the following way:

$m = \frac{m_0}{\sqrt{1-(\frac{v}{10})^{2}}}$

In this framework, Newton's Second Law takes a more general form ($$F$$ denotes the net force applied to the particle):

$F = \frac{d}{dt}(mv)$

The particle is initially at rest before a constant $$\SI{1}{\newton}$$ force is applied to it. At the instant at which $$v = \SI[per-mode=symbol]{5}{\meter\per\second}$$, what is the particle's acceleration (in $$\si[per-mode=symbol]{\meter\per\second\squared}$$) (to 2 decimal places)?

Note: All physical quantities are in standard SI units.

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