Given SHM equation

The displacement is $x = 2\times 10^{-2}\cos(\pi t)\ \text{m}$

Compare with the standard SHM form: $x = A\cos(\omega t)$

So, $A = 2\times 10^{-2}\ \text{m}, \qquad \omega = \pi\ \text{rad/s}$

Find velocity in SHM

Velocity is the time derivative of displacement: $v = \frac{dx}{dt} = -A\omega \sin(\omega t)$

Therefore, $v = -\left(2\times 10^{-2}\right)(\pi)\sin(\pi t)$

Condition for maximum speed

Speed is maximum when $|v|$ is maximum.

Since $|v| = A\omega |\sin(\omega t)|$ it is maximum when $|\sin(\omega t)| = 1$

So, $\sin(\pi t) = \pm 1$

The first time this happens is when $\pi t = \frac{\pi}{2}$

Hence, $t = \frac{1}{2}\ \text{s}$

Check with options

$t = 0.5\,\text{s}$

So the correct option is B.

Comparison with stored answer

Stored correct answer: B

Derived answer: B

They match.