$A$ boy throws balls into the air at a regular interval of $2 \, s$. The next ball is thrown when the velocity of the first ball is zero. How high does the ball rise above his hand (in $, m$)? [Take $g = 9.8 \, m/s^2$]

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.

Free-fall: Discuss the motion of an object under free fall. Neglect air resistance.

The vertical height of point $P$ above the ground is twice that of $Q$. $A$ particle is projected downward with a speed of $5 \, m/s$ from $P$ and at the same time another particle is projected upward with the same speed from $Q$. Both particles reach the ground simultaneously,then:

$A$ man is standing on top of a building $100\, m$ high. He throws two balls vertically,one at $t = 0$ and the other after a time interval $\Delta t$ (less than $2\, s$). The second ball is thrown at a velocity half that of the first. The vertical gap between the first and second ball is $15\, m$ at $t = 2\, s$. The gap is found to remain constant. Calculate the velocity with which the balls were thrown and the exact time interval between their throws.

$A$ body is projected vertically upwards with a velocity of $10\,m/s.$ It reaches the maximum vertical height $h$ in time $t.$ In $\frac{t}{2}$,the height covered is