The curved portions are smooth and horizontal surface is rough. The block is released from P. At what distance from A, it will stop (if $\mu$ = 0.8)?

The distance travelled by the block on the rough surface can be calculated from energy conservation.

$K_i+U_i=K_f+U_f+W_F$

where, W_f  = work done by friction.

$\Rightarrow 0+mgh=0+0+\mu mgs\Rightarrow s=\frac{h}{\mu }=\frac{1}{0.8}=1.25 \mathrm{m}$

The bllock stops at distance 1.25 m from A.