A particle of mass $m$ is at rest at the origin at time $t = 0$. It is subjected to a force $F(t) = F_{0}e^{- bt}$ in the $x$ direction. Its speed $v(t)$ is depicted by which of the following curves

Question

Dr. Abubacker · Accepted Answer

(c) $m\frac{dv}{dt} = F_{0}e^{- bt} \Rightarrow \frac{dv}{dt} = \frac{F_{0}}{m}e^{- bt}$
$\Rightarrow \ \int_{0}^{v}{dv} = \frac{F_{0}}{m}\int_{0}^{t}{e^{- bt}dt}$
$\Rightarrow v = \frac{F_{0}}{m}\left\lbrack \frac{e^{- bt}}{- b} \right\rbrack_{0}^{t}$
$\Rightarrow v = \frac{F_{0}}{mb}(1 - e^{- bt})$

Q. A particle of mass $m$ is at rest at the origin at time $t = 0$. It is subjected to a force $F(t) = F_{0}e^{- bt}$ in the $x$ direction. Its speed $v(t)$ is depicted by which of the following curves

Explanation

Reviewed by Dr. Abubacker

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