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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 - Mathematics

#### 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

##### 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?