To find the maximum velocity attained by the particle, we need to determine the peak of the velocity function. The velocity function is given by V = 3t² - 4t + 4.
The maximum velocity is achieved at the vertex of the parabolic function. The t-coordinate of the vertex can be found using the formula t = -b / (2a), where a and b are the coefficients of the quadratic equation in standard form (at² + bt + c).
In this case, the coefficient of t² is 3 and the coefficient of t is -4. Plugging these values into the formula, we have:
t = -(-4) / (2 * 3) t = 4 / 6 t = 2/3
Now that we have the t-coordinate of the vertex, we can substitute it back into the velocity function to find the maximum velocity:
V = 3(2/3)² - 4(2/3) + 4 V = 3(4/9) - 8/3 + 4 V = 12/9 - 8/3 + 4 V = 4/3 - 8/3 + 4 V = 12/3 V = 4 m/s
Therefore, the maximum velocity attained by the particle is 4 m/s.