A block of mass m is being pulled up a rough incline by an agent delivering constant power P. The coefficient of friction between the block and the incline is \(\mu\). The maximum speed of the block during the course of ascent is :

\(\frac{P}{m.g \sin {\theta} + \mu.m.g \cos {\theta}}\)

Let at any time, the speed of the block along the incline upwards be v.

Newton's Second Law : 

\(\frac{P}{v} - mg \sin {\theta} - \mu mg \cos {\theta} = mv\frac{dv}{dt}\)

For speed to be maximum : \(\frac{dv}{dt} = 0\)

\(v_{max} = \frac{P}{mg \sin {\theta} + \mu. mg \cos {\theta}}\)