Question

A bar starts sliding down an incline of inclination of "alpha". the friction coefficient varies as k=ax where "a" is a constant and "x" is the distance covered. Find the total distance covered and the maximum velocity attained by the bar.

Answer 1

Whenever you encounter a variable force, you have to use integration. Draw the force diagram of the body. Draw a graph of force on the body versus x. The area under this graph gives the total work done. This graph will be a straight line with a negative slope.
First of all, try to find a relation between total force ma on the bar and the distance x covered by it. Try this yourself, and post as soon as you find the relation. If you cant do it, tell me, I will give you more and more hints.

Answer 2

sure.

Answer 3

integrate d equation