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The speed of a particle moving in a circle of radius r=2 {~m}

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Medium

Solving time: 3 mins

The speed of a particle moving in a circle of radius $r = 2 m$ varies with time $t$ as $v = t^{2}$ , where $t$ is in second and $v$ in $m / s$ . Find the radial, tangential and net acceleration at $t = 2 s$ .

Name: Video solution 1: The speed of a particle moving in a circle of radius r=2 m varies with time t as v=t2, where t is in second and v in m/s. Find the radial, tangential and net acceleration at t=2 s.
Uploaded: 2022-10-08T13:11:33.000Z
Duration: 2 min
Description: Video solution 1: The speed of a particle moving in a circle of radius r=2 m varies with time t as v=t2, where t is in second and v in m/s. Find the radial, tangential and net acceleration at t=2 s.

Views: 5,476 students

Updated on: Oct 8, 2022

Book:

Mechanics Volume 1 (DC Pandey)

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Asher Discussed

The speed of a particle moving in a circle of radius

r = 2 m

varies with time

t

v = t^{2}

, where

t

is in second and

v

m / s

. Find the radial, tangential and net acceleration at

t = 2 s

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

Linear speed of particle at

t = 2 s

v = (2)^{2} = 4 m / s

∴

Radial acceleration

a_{r} = \frac{v ^{2}}{r} = \frac{( 4 ) ^{2}}{2} = 8 m / s^{2}

The tangential acceleration is

a_{t} = \frac{d v}{d t} = 2 t

∴

Tangential acceleration at

t = 2 s

a_{t} = (2) (2) = 4 m / s^{2}

∴

Net acceleration of particle at

t = 2 s

a = (a_{r})^{2} + (a_{t})^{2} = (8)^{2} + (4)^{2} or a = 80 m / s^{2}

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Question Text	The speed of a particle moving in a circle of radius $r = 2 m$ varies with time $t$ as $v = t^{2}$ , where $t$ is in second and $v$ in $m / s$ . Find the radial, tangential and net acceleration at $t = 2 s$ .
Updated On	Oct 8, 2022
Topic	Motion in a Plane
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 1
Upvotes	242
Avg. Video Duration	2 min

The speed of a particle moving in a circle of radius $r = 2 m$ varies with time $t$ as $v = t^{2}$ , where $t$ is in second and $v$ in $m / s$ . Find the radial, tangential and net acceleration at $t = 2 s$ .

Text solutionVerified

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The speed of a particle moving in a circle of radius r=2 m varies with time t as v=t2, where t is in second and v in m/s. Find the radial, tangential and net acceleration at t=2 s.

Text solutionVerified

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Practice questions from Mechanics Volume 1 (DC Pandey)

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The speed of a particle moving in a circle of radius $r = 2 m$ varies with time $t$ as $v = t^{2}$ , where $t$ is in second and $v$ in $m / s$ . Find the radial, tangential and net acceleration at $t = 2 s$ .