The figure shows the velocity $(v)$ of a particle plotted against time $(t)$.

$A$ gas balloon is going up with a constant velocity of $10 \text{ m/s}$. When this balloon reached a height of $75 \text{ m}$, a stone is dropped from it and the balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is . . . . . . $\text{m}$. (Take $g = 10 \text{ m/s}^2$)

Two buses $P$ and $Q$ start from a point at the same time and move in a straight line and their positions are represented by $X_{P}(t) = \alpha t + \beta t^{2}$ and $X_{Q}(t) = ft - t^{2}$. At what time,do both the buses have the same velocity?

Which of the following four statements is false?

Fill in the blanks:
$(a)$ Average velocity ....... average speed.
$(b)$ $A$ particle moves in a straight line with an initial velocity $v_0$ and constant acceleration $a$. The formula for the distance covered in the $n^{th}$ second is ............ .
$(c)$ When two objects are moving in the same direction with velocities $v_A$ and $v_B$,the formula for the velocity of $A$ relative to $B$ is .......... .

The relation between time $t$ and distance $x$ is given by $t = \alpha x^2 + \beta x$,where $\alpha$ and $\beta$ are constants. The retardation of the particle is: