$A$ particle is projected upwards with an initial velocity of $80 \; ft/sec$. The particle will be at a height of $96 \; ft$ from the ground after:

$A$ body dropped from the top of a tower falls through $40 \; m$ during the last two seconds of its fall. The height of the tower is ..... $m$.

The given figure shows the $x-t$ plot of one-dimensional motion of a particle. Is it correct to say from the graph that the particle moves in a straight line for $t < 0$ and on a parabolic path for $t > 0$? If not,suggest a suitable physical context for this graph.

From the top of a $64\, ft$ high tower,a stone is thrown upwards vertically with the velocity of $48\, ft/s$. The greatest height (in $ft$) attained by the stone,assuming the value of the gravitational acceleration $g = 32\, ft/s^2$,is

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.

$A$ person standing on the floor of an elevator drops a coin. The coin reaches the floor in time $t_{1}$ if the elevator is at rest and in time $t_{2}$ if the elevator is moving uniformly. Then