Question

A moving body a distance directly proportional to the square of the time. why the acceleration of the body is constant ​

Answer 1

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According to question, distance covered by body is directly proportional to square of the time. e.g.,

x∝t²

$\implies$ x= kt², k is proportionality constant,

$\implies$ Differentiate with respect to t,

$\sf{\dfrac{dx}{dt}}$= 2kt

$\implies$ Again differentiate with respect to time,

$\sf{\dfrac{dx}{dt}}$= 2k

$\implies$ here d²x/dt² is what ? of course acceleration

hence, it is clear that acceleration is

2k = constant