The position of a particle moving along x-axis is related to time `t` as follow: `x=2 t^(2)-t^(3)`, where `x` is in meters and `t` is in seconds.
a. What is the maximum positive displacement of the particle along the `x` axis and at what instant does it attain it?

Explanation

To solve the problem, we will follow these steps:

### Step 1: Write down the position function
The position of the particle is given by the equation:
\[ x(t) = 2t^2 - t^3 \]

### Step 2: Find the velocity function
The velocity \( v(t) \) is the derivative of the position function with respect to time \( t \):
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