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The Equation of Motion of a Particle is S = 2t2 + Sin 2t, Where S is in Metres and T is in Seconds. the Velocity of the Particle When Its Acceleration is 2 M/Sec2, is (A) π + √ 3 M / Sec - CBSE (Science) Class 12 - Mathematics

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Question

The equation of motion of a particle is s = 2t2 + sin 2t, where s is in metres and is in seconds. The velocity of the particle when its acceleration is 2 m/sec2, is

  • \[\pi + \sqrt{3} m\ /\sec\]

  • \[\frac{\pi}{3} + \sqrt{3} m/\sec\]

  • \[\frac{2\pi}{3} + \sqrt{3} m/\sec\]

  • \[\frac{\pi}{3} + \frac{1}{\sqrt{3}} m/\sec\]

Solution

 \[\frac{\pi}{3} + \sqrt{3} \ m/\sec\]

\[\text { According to the question },\] 
\[s = 2 t^2  + \sin  2t\] 
\[ \Rightarrow \frac{ds}{dt} = 4t + 2  \cos  2t\] 
\[ \Rightarrow \frac{d^2 s}{d t^2} = 4 - 4  \sin  2t\] 
\[ \Rightarrow 4 - 4  \sin  2t = 2\] 
\[ \Rightarrow 4  \sin  2t = 2\] 
\[ \Rightarrow \sin  2t = \frac{1}{2}\] 
\[ \Rightarrow 2t = \frac{\pi}{6}\] 
\[\text { Now,} \] 
\[\frac{ds}{dt} = 4\left( \frac{\pi}{12} \right) + 2  \cos\left( \frac{\pi}{6} \right)\] 
 
\[ \Rightarrow \frac{ds}{dt} = \frac{\pi}{3} + \sqrt{3}  m/\sec\] 
  Is there an error in this question or solution?
Solution The Equation of Motion of a Particle is S = 2t2 + Sin 2t, Where S is in Metres and T is in Seconds. the Velocity of the Particle When Its Acceleration is 2 M/Sec2, is (A) π + √ 3 M / Sec Concept: Rate of Change of Bodies Or Quantities.
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