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NEET 2007
Exam
NEET
Year
2007
Subject
Physics
Chapter
Motion in One Dimension

NEET 2007 · Physics · Motion in One Dimension

The position x of a particle with respect to time t along x -axis...

The position xx of a particle with respect to time tt along xx-axis is given by x=9t2x=9 t^2 −t3-t^3 where xx is in metres and tt in second. What will be the position of this particle when it achieves maximum speed along the +x+x direction?

Options

  1. A54 m54 \mathrm{~m}
  2. B81 m81 \mathrm{~m}
  3. C24 m24 \mathrm{~m}
  4. D32 m32 \mathrm{~m}.

Correct answer

A. 54 m54 \mathrm{~m}

Step-by-step solution

It is given that x=9t2−t3v=dxdt=18t−3t2dvdt=a=18−6t\begin{aligned} x & =9 t^2-t^3 \\ v & =\frac{d x}{d t}=18 t-3 t^2 \\ \frac{d v}{d t} & =a=18-6 t \end{aligned} for maximum speed dvdt=0andd2vdt2\frac{d v}{d t}=0 and \frac{d^2 v}{d t^2} negative So 18−6t=0⇒t=3s18-6 t=0 \Rightarrow \quad t=3 s at t=3s,x=9(3)2−(3)3=81−27=54 m\quad t=3 s, x=9(3)^2-(3)^3 =81-27=54 \mathrm{~m}
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