$A$ particle is thrown vertically upwards with a velocity of $4\,ms^{-1}$. The ratio of its accelerations after $1\,s$ and $2\,s$ of its motion is

Write the equation for the distance covered by an object falling freely during the $n^{th}$ second.

$A$ body dropped from a height $h$ with an initial speed zero,strikes the ground with a velocity $3 \ km/h$. Another body of the same mass is dropped from the same height $h$ with an initial speed of $4 \ km/h$. Find the final velocity of the second body with which it strikes the ground in $km/h$.

$Assertion$ : Two balls of different masses are thrown vertically upward with the same speed. They will pass through their point of projection in the downward direction with the same speed.
$Reason$ : The maximum height and downward velocity attained at the point of projection are independent of the mass of the ball.

$A$ stone falls from a balloon that is descending at a uniform rate of $12 \, m/s$. The displacement of the stone from the point of release after $10 \, s$ is.......$m$ $(g = 9.8 \, m/s^2)$

$A$ body is dropped from a certain height $h$ ($h$ is very large) and a second body is thrown downward with a velocity of $5 \, m/s$ simultaneously. What will be the difference in the heights of the two bodies after $3 \, s$?