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

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The maximum power exerted by train A, defined as Pv^{3/2}, is influenced by its mass and velocity, with resistance to motion represented as kv. The equation of motion at full power is expressed as Pv^{1/2} - kv = m(dv/dt), highlighting the balance between power output and resistive forces. The relationship between force and power is crucial, as power is the rate at which work is done, linking directly to the force applied and the velocity of the train. Understanding these dynamics is essential for analyzing train performance and efficiency. The discussion emphasizes the importance of power in determining motion equations for trains.
grusini
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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}?
 
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Hi grusini,

grusini said:
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?
 

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