Question

What is the position at any time, for a body starting from rest, with an acceleration
a=at2

Answer 1

Given,

acceleration of the body = at².

Now, velocity at any time

dv = a dt

=> dv = at² dt

integrating both side

v = at³/3

Now,

ds = v dt

=>ds = at³/3 dt

=>s = at⁴/12 Ans.