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Motion in Straight Line

Graphical representation of motion

A particle of mass m is at rest at the origin at time t=0. It

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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?

Views: 5,994 students

Updated on: Apr 30, 2023

Book:

Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Exam:

JEE Mains 2012

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Isabella Discussed

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?

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

As the force is exponentially decreasing, so its acceleration, i.e., rate of increase of velocity will decrease with time. Thus, the graph of velocity will be an increasing curl with decreasing slope with time.

∴ a = \frac{F}{M} = \frac{F _{0}}{m} e^{- b t} = \frac{d v}{d t}

\Rightarrow \int_{0}^{v} d v = \int_{0}^{t} \frac{F _{0}}{m} e^{- b t} d t

\Rightarrow v = \frac{F _{0}}{m} [(\frac{1}{- b}) e^{- b t}]_{0}^{t} = \frac{F _{0}}{mb} [e^{- b t}]_{t}^{0}

= \frac{F _{0}}{mb} (e^{0} - e^{- b t}) = \frac{F _{0}}{mb} (1 - e^{- b t})

v_{m a x} = \frac{F _{0}}{mb}

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Question Text	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?
Updated On	Apr 30, 2023
Topic	Motion in Straight Line
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 9
Upvotes	893
Avg. Video Duration	7 min

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?

Text solutionVerified

Filo tutor solutions (9)

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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?

Text solutionVerified

Filo tutor solutions (9)

Questions from JEE Mains 2012 - PYQs

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Practice questions on similar concepts asked by Filo students

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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?