If the velocity of the a particle moving on x-axis is given by `v=3t^(2)-12 t +6.` at what time is the acceleration of particle zero ?

Options

A. 2 sec
B. `2+sqrt(2) sec`
C. `2-sqrt(2) sec`
D. zero

Explanation

To find the time at which the acceleration of the particle is zero, we need to follow these steps:

### Step 1: Write down the given velocity function.
The velocity \( v \) of the particle is given by:
\[ v = 3t^2 - 12t + 6 \]

### Step 2: Determine the acceleration function.
Acceleration \( a \) is the derivative of velocity with respect to time \( t \). Therefore, we differentiate the velocity function:
\[ a = \frac{dv}{dt} = \frac{d}{dt}(3t^2 - 12t + 6) \]
Using the power rule of differentiation:
\[ a = 6t - 12 \]

### Step 3: Set the acceleration equal to zero.
To find when the acceleration is zero, we set the acceleration function to zero:
\[ 6t - 12 = 0 \]

### Step 4: Solve for \( t \).
Now, we solve for \( t \):
\[ 6t = 12 \]
\[ t = \frac{12}{6} = 2 \]

### Conclusion:
The acceleration of the particle is zero at \( t = 2 \) seconds.