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 depict - Physics MCQ AIEEE 2012 2026 | ExamTest.live

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1 mark

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?

Solution & Step-by-step Explanation

F (t) = m \frac{d v}{d t} = F_{0} e^{- b t} \frac{d v}{d t} = \frac{F _{0}}{m} e^{- b t} d v = \frac{F _{0}}{m} e^{- b t} d t Integrating from v = 0 at t = 0 : \int_{0}^{v (t)} d v = \frac{F _{0}}{m} \int_{0}^{t} e^{- b t} d t v (t) = \frac{F _{0}}{m} [\frac{e ^{- b t}}{- b}]_{0}^{t} = \frac{F _{0}}{mb} [- e^{- b t} - (- 1)] v (t) = \frac{F _{0}}{mb} (1 - e^{- b t}) At t = 0, v (0) = \frac{F _{0}}{mb} (1 - 1) = 0 .As t \to \infty, v (t) \to \frac{F _{0}}{mb} .This corresponds to an increasing curve that levels off at a horizontal asymptote.

Try it yourself before checking the explanation above.

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?

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