How Does Train A's Maximum Power Influence Its Equation of Motion?

[grusini]

The maximum power that a train $$A$$ of mass $$m$$ can exert when traveling at a velocity $$v$$ is $$Pv^{3/2}$$ where $$P$$ is a constant. The resistance to motion is $$kv$$.

Why is the equation of motion of $$A$$ at full power given by: $$Pv^{1/2}-kv=m\frac{dv}{dt}$$?

 

[alphysicist]

Hi grusini,

The maximum power that a train $$A$$ of mass $$m$$ can exert when traveling at a velocity $$v$$ is $$Pv^{3/2}$$ where $$P$$ is a constant. The resistance to motion is $$kv$$.

Why is the equation of motion of $$A$$ at full power given by: $$Pv^{1/2}-kv=m\frac{dv}{dt}$$?

What is the relationship between force and power?