Equations of Motion: Solving the Problem and Finding Velocity Limits

[Logarythmic]

The problem is to determine the equation of motion for a point particle on which both the gravitational force and a friction force of magnitude
|\vec{F}_fr| = k|\vec{v}|
act and to show that when the particle starts at rest, its velocity cannot exceed mg/k.
I have attached my calculations but something is wrong. The velocity cannot increase when the incline is almost flat..?

 

[quasar987]

Incline? You can't be on an incline since additionally, there is a normal force. The problem makes no mention of such thing.

Just solve the equation of motion for F=Fgrav-kv. Plug in the initial value v0=0 and show that v(t) is a monotonous function that converge assymptotically towards mg/k as t-->+infty.

 

[Logarythmic]

Of course. Thanks :)