Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Medical
  • The motion of a body is given by the equation   where <img alt="v" src

The motion of a body is given by the equation  \frac{dv}{dt}=6-3v where v is the speed in m{{s}^{-1}} and t is the time in second. The body is at rest at t=0. The speed varies with time as

Option: 1

v=(1-{{e}^{-3t}})


Option: 2

v=2(1-{{e}^{-3t}}).


Option: 3

v=(1+{{e}^{-2t}})


Option: 4

v=2(1+{{e}^{-2t}})


Answers (1)

best_answer

\frac{dv}{dt}=6-3v

dt=\frac{dv}{6-3v}

Integrating both sides, we get t=-\frac{1}{3}\ln (6-3v)+C

Where C is the constant of integration

At t=0,v=0

\therefore C=\frac{1}{3}\ln 6

\therefore t=-\frac{1}{3}\ln (\frac{6-3v}{6})

{{e}^{-3t}}=1-\frac{1}{2}v

v=2(1-{{e}^{-3t}})

Posted by

avinash.dongre

View full answer

NEET 2024 Most scoring concepts

    Just Study 32% of the NEET syllabus and Score up to 100% marks

Similar Questions

Trending Articles/News

anam-khan

From 589 to 41: NEET candidate misses cut-off over silly error, HC orders re-checking of OMR sheet
anam-khan

CENTAC Puducherry’s NEET counselling rules ‘discriminatory’; Doctors with Disabilities demand revision
anam-khan

Telangana NEET UG 2025 merit list out; 43,400 qualify for MBBS, BDS counselling

Latest Question