If a body starts from rest and moves with uniform acceleration, what is the ratio of distances cover

Question

If a body starts from rest and moves with uniform acceleration, what is the ratio of distances covered by it in the 1st second, 2nd second, and 3rd second?

Professor PC Thomas Classes · Answer

The distance covered in the $n$-th second is $s_n = \frac{a}{2}(2n - 1)$. For $n=1$, $s_1 = \frac{a}{2}(1)$. For $n=2$, $s_2 = \frac{a}{2}(3)$. For $n=3$, $s_3 = \frac{a}{2}(5)$. Thus, the ratio is $1 : 3 : 5$.