I was trying to create a problem yesterday, something like this:
The yellow region represents a smooth surface, while brown represents the rough one.
The coefficient of friction between the block and the rough surface varies as , where is the distance traversed by the block on the rough surface (assuming the intersection of the axes looking lines as the origin) and is a positive constant.
As an initial approach, I tried to find out the stopping distance of the block, which goes like this.
or as the only force acting on the block is friction.
But couldn't proceed on to evaluate time of motion. Please help me, thanks.
PS: Please rectify if there's any mistake in evaluating stopping distance.