A particle of mass m is at rest at the origin at time t = 0. It is subjected to a force F(t) = F0e-bt in the x direction. Its speed v(t) is depicted by which of the following curves ?

Question

A particle of mass m is at rest at the origin at time t = 0. It is subjected to a force F(t) = F0e-bt in the x direction. Its speed v(t) is depicted by which of the following curves ? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

F = ma = F0 e-bt (dv/dt)=(F0/m) e-bt ∫ limitsv0dv=(F0/m)∫ limitst0e-btdt v=(F0/m)[(e-bt/-b)]t0 v=(F0/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 $F (t) = F_{0} e^{- b t}$ in the $x$ direction. Its speed $v (t)$ is depicted by which of the following curves ?

$F = ma = F_{0} e^{- b t}$
$\frac{d v}{d t} = \frac{F _{0}}{m} e^{- b t}$
$0 \int v$ $d v = \frac{F _{0}}{m}$ $0 \int t$ $e^{- b t} d t$
$v = \frac{F _{0}}{m} [\frac{e ^{- b t}}{- b}]_{_{_{0}}}^{t}$
$v = \frac{F _{0}}{mb} (1 - e^{- b t})$

Q. A particle of mass m is at rest at the origin at time t=0. It is subjected to a force F(t)=F0​e−bt in the x direction. Its speed v(t) is depicted by which of the following curves ?

F=ma=F0​e−bt dtdv​=mF0​​e−bt 0∫v​dv=mF0​​0∫t​e−btdt v=mF0​​[−be−bt​]0​​t​ v=mbF0​​(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 $F (t) = F_{0} e^{- b t}$ in the $x$ direction. Its speed $v (t)$ is depicted by which of the following curves ?

$F = ma = F_{0} e^{- b t}$
$\frac{d v}{d t} = \frac{F _{0}}{m} e^{- b t}$
$0 \int v$ $d v = \frac{F _{0}}{m}$ $0 \int t$ $e^{- b t} d t$
$v = \frac{F _{0}}{m} [\frac{e ^{- b t}}{- b}]_{_{_{0}}}^{t}$
$v = \frac{F _{0}}{mb} (1 - e^{- b t})$