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.

中文翻译：

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恒定功率耗散运动

我们分析了由恒定功率推动并受到耗散力的粒子的速度。我们考虑耗散过程的三种情况：干摩擦和粘性阻力在线性和二次依赖于速度的状态下。我们导出运动方程，然后基于合理的图形分析，确定速度曲线的定性形状作为时间的函数。最后，我们求解粒子速度的运动方程并确认先前的结果。我们进行这项工作的动机之一是普遍存在的现象：当车辆以相当恒定的功率推动时，车辆达到几乎恒定的速度。