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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