Distance in successive equal time intervals

A body moves with constant acceleration and the question asks for distance covered in the nth second, in successive time intervals, or ratios of distances in consecutive equal intervals.

jee-main 2022 Q1 View
A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10 m in $t$ s, the distance travelled by the toy in the next $t$ s will be:
(1) 10 m
(2) 20 m
(3) 30 m
(4) 40 m
jee-main 2024 Q21 View
The displacement and the increase in the velocity of a moving particle in the time interval of $t$ to $( t + 1 )$ s are 125 m and $50 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, respectively. The distance travelled by the particle in $( t + 2 ) ^ { \text {th} } \mathrm { s }$ is $\_\_\_\_$ m.
jee-main 2024 Q21 View
A body moves on a frictionless plane starting from rest. If $S_n$ is distance moved between $t = n-1$ and $t = n$ and $S_{n-1}$ is distance moved between $t = n-2$ and $t = n-1$, then the ratio $\frac{S_{n-1}}{S_n}$ is $\left(1 - \frac{2}{x}\right)$ for $n = 10$. The value of $x$ is $\_\_\_\_$.