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

Let x be the position at time instant t of the particle in motion. Given `x=kt^(3)`, where k is a constant of proportionality. The velocity of particle can be calculated as `v=(dx)/(dt)=3kt^(2)` and acceleration of object can be calculated as
`a=(dv)/(dt)=(d)/(dt){3kt^(2)]=3k(d)/(dt)(t^(2))`
`a=3k(2t^(2-1))=6kt`
i.e., `a prop t`. It means acceleration `prop` time.