Velocity of a Body on Reaching the Bottom of a Rough Inclined Plane

Body on a rough inclined plane acquires a certain velocity on reaching the bottom of a rough inclined plane. Let the body is starting from the state of rest. We know that body on rough inclined plane will move only when the down ward force that is the component of weight is able to dominate the limiting frictional force. You can check the at here at Motion of a body on a Rough Inclined Plane an Introduction.

We have further derive equation for the acceleration of a body sliding down on rough inclined plane in the following post at Acceleration of a body sliding down on a rough inclined plane.

We can use equation of motion to find final velocity of the body.In the place of acceleration of the body, We can substitute the derived equation.The equation is in terms of length and it can be converted into inclined angle and height.

If the surface is smooth, we can equate the coefficient of friction to zero, the equation can be further simplified and the velocity acquired by the body is equal to the velocity acquired by a freely falling body.