A displacement of a body executing SHM is given by x = A sin(2π t + π/3). The first time from t = 0 when the velocity is maximum is:
(A) 0.33 sec
(B) 0.16 sec
(C) 0.25 sec
(D) 0.5 sec

To find the time when the velocity of a body undergoing simple harmonic motion (SHM) is maximum, we need to differentiate the displacement equation with respect to time (t) to get the velocity equation and then find when the velocity is maximum.

Given displacement equation:
x = A * sin(2πt + π/3)

Let's find the velocity (v) by taking the derivative of the displacement equation with respect to time (t):

v = dx/dt = d/dt [A * sin(2πt + π/3)]

Using the chain rule for differentiation, we have:

v = A * d/dt [sin(2πt + π/3)]

Now, differentiate sin(2πt + π/3) with respect to t:

v = A * 2π * cos(2πt + π/3)

To find the maximum velocity, we need to find when the cosine term is at its maximum value, which is 1. The cosine function reaches its maximum value at multiples of 2π, so:

2πt + π/3 = 2nπ, where n is an integer

Solving for t:

2πt = 2nπ - π/3
t = (2nπ - π/3) / (2π)

Now, we want to find the first time (t) when the velocity is maximum, which corresponds to the smallest positive value of t. So, let n = 0:

t = (2(0)π - π/3) / (2π)
t = (-π/3) / (2π)
t = -1/6

Since we are looking for the first positive value of time, we take the positive portion of this result:

t = 1/6

So, the first time when the velocity is maximum is t = 1/6 seconds.

Therefore, the correct answer is (A) 0.33 seconds.