$A$ ball is thrown vertically upwards. Which of the following plots represents the speed-time graph of the ball during its flight if air resistance is not ignored?

$A$ body thrown vertically upwards from the ground reaches a maximum height $H$. The ratio of the velocities of the body at heights $\frac{3H}{4}$ and $\frac{8H}{9}$ from the ground is

If a freely falling body travels in the last second a distance equal to the distance travelled by it in the first three seconds,the time of the travel is ........ $sec$.

Galileo's law of odd numbers: "The distances traversed, during equal intervals of time, by a body falling from rest, stand to one another in the same ratio as the odd numbers beginning with unity [namely, $1: 3: 5: 7 \ldots$]". Prove it.

$A$ particle is dropped from the top of a tower. The distance covered by it in the last one second is equal to the distance covered by it in the first three seconds. The height of the tower is $....m$

$A$ ball is thrown up vertically with a certain velocity so that it reaches a maximum height $h$. Find the ratio of the times at which it is at height $\frac{h}{3}$ while going up and coming down respectively.