$v =\frac{ dS }{ dt }= v _0 e ^{- t / t }$
$\int_0^{ s } dS = v _0 \int_0^\tau e ^{- t / t } dt$
$\Delta S = v _0\left[-\tau e ^{- t / \tau }\right]_0^{ t }$
$\Delta S = v _0 \tau\left[1-\frac{1}{ e }\right]$
$\text { Impulse }=\Delta P = m \Delta v$
$\Delta v =\frac{1}{0.4}=2.5$
$\Delta s =4 \times 2.5[1-0.37]=10 \times 0.63=6.3 m / s$
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The correct option ($s$) is (are)
$(A)$ $q_{A C}=\Delta U_{B C}$ and $W_{A B}=P_2\left(V_2-V_1\right)$
$(B)$ $\mathrm{W}_{\mathrm{BC}}=\mathrm{P}_2\left(\mathrm{~V}_2-\mathrm{V}_1\right)$ and $\mathrm{q}_{\mathrm{BC}}=\mathrm{H}_{\mathrm{AC}}$
$(C)$ $\Delta \mathrm{H}_{\mathrm{CA}}<\Delta \mathrm{U}_{\mathrm{CA}}$ and $\mathrm{q}_{\mathrm{AC}}=\Delta \mathrm{U}_{\mathrm{BC}}$
$(D)$ $\mathrm{q}_{\mathrm{BC}}=\Delta \mathrm{H}_{\mathrm{AC}}$ and $\Delta \mathrm{H}_{\mathrm{CA}}>\Delta \mathrm{U}_{\mathrm{CA}}$
