1. Find the velocity function by differentiating the displacement function with respect to time:

x(t) = t^3 - 6t^2 + 3t + 4

v(t) = dx/dt = 3t^2 - 12t + 3

2. Find the acceleration function by differentiating the velocity function with respect to time:

a(t) = dv/dt = 6t - 12

3. Set the acceleration to zero and solve for time t:

6t - 12 = 0

6t = 12

t = 2

4. Substitute the value of t back into the velocity function to find the velocity when acceleration is zero:

v(2) = 3(2)^2 - 12(2) + 3

v(2) = 3(4) - 24 + 3

v(2) = 12 - 24 + 3

v(2) = -9