The equation of a particle executing simple harmonic motion is given by $$x = \sin\pi\left(t + \frac{1}{3}\right)$$ m. At $$t = 1$$ s, the speed of particle will be (Given: $$\pi = 3.14$$)

The equation of motion is $$x = \sin\pi\left(t + \frac{1}{3}\right)$$ m.

Find the velocity by differentiating.

$$v = \frac{dx}{dt} = \pi\cos\pi\left(t + \frac{1}{3}\right)$$ m/s

Substitute $$t = 1$$ s.

$$v = \pi\cos\pi\left(1 + \frac{1}{3}\right) = \pi\cos\left(\frac{4\pi}{3}\right)$$

Evaluate $$\cos\left(\frac{4\pi}{3}\right)$$.

$$\frac{4\pi}{3} = \pi + \frac{\pi}{3}$$, which lies in the third quadrant.

$$\cos\left(\frac{4\pi}{3}\right) = -\cos\left(\frac{\pi}{3}\right) = -\frac{1}{2}$$

Calculate the speed.

$$v = \pi \times \left(-\frac{1}{2}\right) = -\frac{\pi}{2}$$ m/s

Speed $$= |v| = \frac{\pi}{2} = \frac{3.14}{2} = 1.57$$ m/s $$= 157$$ cm/s

The correct answer is Option A.