Answer
Distance measured is S.
Speed at the final point is v=0. Initial velocity is $v_{0}$.
$v^{2}=v_{0}^{2}+2aS$
Now, $a=\frac{F_{f}}{m}=\frac{coefficient \,of \,friction \times mg}{m}$
$a=coefficient\, of\, friction \times g$
Thus, from $v^{2}=v_{0}^{2}+2aS$,
Coefficient of friction $\times g=a=-\frac{v_{0}^{2}}{2S}$
Coefficient of friction = $-\frac{v_{0}^{2}}{2gS}$
The minus sign indicates that the direction of the friction force is opposite to that of the velocity.
Work Step by Step
Distance measured is S.
Speed at the final point is v=0. Initial velocity is $v_{0}$.
$v^{2}=v_{0}^{2}+2aS$
Now, $a=\frac{F_{f}}{m}=\frac{coefficient \,of \,friction \times mg}{m}$
$a=coefficient\, of\, friction \times g$
Thus, from $v^{2}=v_{0}^{2}+2aS$,
Coefficient of friction $\times g=a=-\frac{v_{0}^{2}}{2S}$
Coefficient of friction = $-\frac{v_{0}^{2}}{2gS}$
The minus sign indicates that the direction of the friction force is opposite to that of the velocity.
