We analyse the velocity of a particle propelled by a constant power and subjected to a dissipative force. We consider three cases of dissipative processes: dry friction and viscous drag in the regime of linear and quadratic dependence on velocity. We derive the equation of motion and then, based on a rational and graphical analysis, determine the qualitative shape of the velocity curve as a function of time. Finally, we solve the equation of motion for the particle’s velocity and confirm the previous result. One of our motivations for this work is the ubiquitous phenomenon of vehicles reaching a nearly constant velocity when propelled by a fairly constant power.
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