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)

Answer: (b). mdv/dt = F₀e-bt ⇒ v = ∫₀t F₀/me-btdt = F₀/mb(1 - e-bt) v starts at 0, always increases (force stays positive) and approaches F₀/mb as t → ∞. So the answer is (b).

A particle of mass m is at rest at the origin at time t = 0 It is… | JEE Main 2012 (AIEEE)

Q37JEE Main 2012 · AIEEEMedium

Inertia, First & Second Laws

A particle of mass $m$ is at rest at the origin at time $t = 0$ It is subjected to a force $F(t) = F_0e^{-bt}$ in the $x$ direction. Its speed $v(t)$ is depicted by which of the following curves?

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Answer: (b)

$m\frac{dv}{dt} = F_0e^{-bt} \Rightarrow v = \int_0^t \frac{F_0}{m}e^{-bt}dt = \frac{F_0}{mb}\left(1 - e^{-bt}\right)$
$v$ starts at 0, always increases (force stays positive) and approaches $\frac{F_0}{mb}$ as $t \to \infty$ .
So the answer is (b).

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