Question

18. A bus starts from rest
kinetic friction
proportional to
from rest and travels a distance s along a straight horizontal road. The coefficients of stau
c friction between the road and the tyres ar
es are us and uk respectively. The minimum time of travel is proportional to

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Answer 1

Answer:

$t\ \propto\ \sqrt{\dfrac{1}{\mu}$

Explanation:

Given,

* Initial velocity of the bus = u = 0

let 'a' be the acceleration of the bus, and the force acting on the bus is frictional force,

Therefore,

$F\ =\ fs\\\Rightarrow ma\ =\ \mu N\ =\ \mu mg\\\Rightarrow a\ =\ \mu g$

Now from the kinematic equation of displacement,

$s= ut\ +\ \dfrac{1}{2}at^2\\\Rightarrow s\ =\ 0\ +\ \dfrac{1}{2}at^2\\\Rightarrow t\ =\ \sqrt{\dfrac{2s}{a}}\\\Rightarrow t\ =\ \sqrt{\dfrac{2s}{\mu g}}\\\Rightarrow t\ \propto\ \sqrt{\dfrac{1}{\mu}}$

Hence $\mu$ varies with $\mu_s\ and\ \mu_k$ if the body is at rest or in moving.  

Hence, the time of travel is inversely  proportional to the squire root of the coefficient  of static or kinetic friction,