A block is projected with speed $20 \,m / s$ on a rough horizontal surface. The coefficient of friction $(\mu)$ between the surfaces varies with time $(t)$ as shown in figure. The speed of body at the end of $4$ second will be ............ $m / s$ ( $g=$ $10 \,m / s ^2$ )
Difficult
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(a)
Retardation
$\frac{d v}{d t}=-\mu g$
$\int d v=-\int \mu g d t$
$\Delta v=-g \int \mu d t$
$\int \mu d t$ is area under $\mu-t$ curve
$v-20=-10\left(2 \frac{1}{2}+\frac{1}{2}(2)(0.2)+(2)(0.3)\right)$
$v=20-18=2 \,m / s$
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