Question

An insect of mass 'm' is initially at one end of a stick of length 'l' and mass 'M'.The coefficient of friction between the insect and the stick is 'k'. The minimum time in which the insect can reach the other end of the stick is 't', then `t^2`?

Answer 1

Given that the mass of the insect is `m` .

Considering that the stick on which the insect moves is in horizontal position.
The normal reaction on the insect will be equal to its weight `mg`, where `g` represents acceleration due to gravity,

Hence the maximum frictional force will be `kmg`, where `k` is the coefficient of friction. So the maximum reactionary force that can be obtained for the movement of the insect is `kmg`.
Hence the maximum acceleration with which the insect can move over this stick will be `a=(kmg)/m=kg`
Starting from rest if the insect takes minimum time `t` (as it is moving with maximum acceleration `a`) to cover whole length `l` of the stick, then by the equation of kinematics we can write
`l=0xxt+1/2axxt^2`
`=>t^2=(2l)/a=(2l)/(kg)`