The position of a particle moving on a straight line is proportional to the cube of the time elapsed. How does the acceleration of the particle depend on time elapsed?

Explanation

To solve the problem, we need to find how the acceleration of a particle depends on the time elapsed, given that the position of the particle is proportional to the cube of the time elapsed.

### Step-by-Step Solution:

1. **Understanding the relationship between position and time:**
We are given that the position \( x \) of the particle is proportional to the cube of the time \( t \). We can express this relationship mathematically as:
\[
x = k t^3
...