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JEE Main 2011
Exam
JEE Main
Year
2011
Subject
Physics
Chapter
Motion in One Dimension

JEE Main 2011 · Physics · Motion in One Dimension

An object, moving with a speed of 6.25 ~m / s , is decelerated at a...

An object, moving with a speed of 6.25 m/s6.25 \mathrm{~m} / \mathrm{s}, is decelerated at a rate given by : dvdt=−\frac{\mathrm{dv}}{\mathrm{dt}}=-2.5 v\sqrt{\mathrm{v}}where vv is the instantaneous speed. The time taken by the object, to come to rest, would be:

Options

  1. A2 s2 \mathrm{~s}
  2. B4 s4 \mathrm{~s}
  3. C8 s8 \mathrm{~s}
  4. D1 s1 \mathrm{~s}

Correct answer

A. 2 s2 \mathrm{~s}

Step-by-step solution

dvdt=−\frac{d v}{d t}=-2.5 v\sqrt{v}Integrating the above equation. \Rightarrow 2 v=−\sqrt{v}=-2.5 t+C\mathrm{t}+\mathrm{C}at t=0,v=6.25⇒C=5\mathrm{t}=0, \mathrm{v}=6.25 \Rightarrow \mathrm{C}=5 at v=0⇒t=52.5=2 sv=0 \Rightarrow t=\frac{5}{2.5}=2 \mathrm{~s}
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