#### Question

The equation of motion of a particle is *s* = 2*t*^{2} + sin 2*t*, where *s* is in metres and *t *is in seconds. The velocity of the particle when its acceleration is 2 m/sec^{2}, is

##### Options

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

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

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

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

#### 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?

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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 Concept: Rate of Change of Bodies Or Quantities.

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