Question

A small body is projected with a velocity of $20.5m{s}^{-1}$ along rough horizontal surface. The coefficient of friction $\left(\mu \right)$ between the body and surface changes with time $t$ (in s) as the body moves along the surface. The velocity at the end of 4 $s$ in $m/s$ .Write upto two digits after the decimal point.

Answer 1

Impulse $=\int \overrightarrow{F}dt=m(\overrightarrow{v_f}-\overrightarrow{v_i})$
where $v_f$ and $v_i$ are final and initial velocity respecgtively. We know that area under $\mu -t$ curve multiplied by $mg$ gives change in momentum.
$-mg\times Areaunder\mu -tgraph=m(v_f-20.5)$
$-mg\times \left[\frac{1}{2}\right(0.4+0.3)\times 1+0.4\times 2+\frac{1}{2}(0.4+0.2)\times 1]=m(v_f-20.5)$
$v_f=6m/s$