Low-Speed Lorentzian Physics

Consider a particle with rest-mass (m0=1 kg)(m_0 = \SI{1}{\kilo\gram}) and velocity vv. Suppose we're in an alternate universe in which the "cosmic speed limit" is only 10 m/s\SI[per-mode=symbol]{10}{\meter\per\second}, and that the particle's mass varies with its velocity in the following way:

m=m01(v10)2m = \frac{m_0}{\sqrt{1-(\frac{v}{10})^{2}}}

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

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

The particle is initially at rest before a constant 1 N\SI{1}{\newton} force is applied to it. At the instant at which v=5 m/sv = \SI[per-mode=symbol]{5}{\meter\per\second}, what is the particle's acceleration (in m/s2\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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