Question

A vehicle of mass 500 kg moving with a velocity of 20m/s on a straight , horizontal road comes to rest in a distance of 100 m after the fuel is cut off. Find the coefficient of kinetic friction between the tyres of the vehicle & the road

Answer 1

Here,

$\displaystyle\longrightarrow\sf {m=500\ kg}$

$\displaystyle\longrightarrow\sf {u=20\ m\ s^{-1}}$

$\displaystyle\longrightarrow\sf {v=0\ m\ s^{-1}}$

$\displaystyle\longrightarrow\sf{s=100\ m}$

The retardation exerted on the vehicle, by third kinematic equation,

$\displaystyle\longrightarrow\sf {a=\dfrac {v^2-u^2}{2s}}$

$\displaystyle\longrightarrow\sf{a=\dfrac {0^2-20^2}{2\times 100}}$

$\displaystyle\longrightarrow\sf {a=-2\ m\ s^{-2}}$

Then, the frictional force acting on the vehicle,

$\displaystyle\longrightarrow\sf {f=ma}$

$\displaystyle\longrightarrow\sf {f=500\times-2}$

$\displaystyle\longrightarrow\sf {\underline {\underline {f=-1000\ N}}}$

$\displaystyle\longrightarrow\sf {\underline {\underline {f=-1\ kN}}}$