Question

A small body is projected with a velocity of $20.5{\text{ms}}^{-1}$ on a rough horizontal surface. The coefficient of friction $\left(\mu \right)$ between the surface changes with time ($t$ in $\text{s}$) as the body moves along the surface. The velocity at the end of $4\text{s}$ in ${\text{ms}}^{-1}$ will be

. (take $g=10{\text{ms}}^{-2}$)

Answer 1

$F=-\mu mg\Rightarrow a=-\mu g$
$\because \int dv=-g\int \mu dt$
$\Delta v=-g\int \mu dt=-g(\text{area under}\mu -t\text{curve}$
Here $\text{area under}\mu -t\text{curve}=1.45$
$\therefore$ velocity after $4\text{s}$ $=20.5-\left(1.45\right)10=6\text{m/s}$