FIITJEE AITS QUESTION

something must be wrong in my concepts:i still cant figure out this q. Help!!

An insect of mass m is initially at rest at one end of a stick of length L and mass M , which rests on a smooth horizontal floor . The coefficient of friction between insect and stick is k. The insect starts moving to reach the other end in the shortest possible time

A)The center of mass of the plank has speed v=root under(kmg/M)
b)time taken by insect to reach the other end is: t=root under(2LM/k(M+m)g)
c)The magnitude of linear momentum of the insect at time t = kmgt
d)max speed acquired by stick is : root under( 2kLMm²g(M+m)g )

The ans are : a,b,c