The length covered by a body is found to be directly proportional to the square of time. What is the nature of acceleration?

Given that x α t², where x is displacement of body and t is time

on removing α sign, x=bt² ... 1 ... where b is proportionality constant

now differentiating 1 with respect to time we get,

v=2bt where v is velocity

now on further differentiating we get,

a=2b where a is acceleration

it means acceleration of body is constant, it is independent of time