$A$ 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 $g = 10 \text{ m/s}^2$)

$A$ ball moves one-fourth of a circle of radius $R$ in time $T$. Let $v_1$ and $v_2$ be the magnitudes of mean speed and mean velocity vector. The ratio $\frac{v_1}{v_2}$ will be

The displacement of a particle moving in a straight line depends on time as $x = \alpha t^3 + \beta t^2 + \gamma t + \delta$. The ratio of initial acceleration to its initial velocity depends on:

$A$ metro train starts from rest and in $5 \, s$ achieves $108 \, km/h$. After that,it moves with constant velocity and comes to rest after travelling $45 \, m$ with uniform retardation. If the total distance travelled is $395 \, m$,then the total time of travelling is ....... $s$.

State whether the following statements are true or false:
$(a)$ If the motion is not along a straight line,then path length = magnitude of displacement.
$(b)$ Stopping distance is directly proportional to the initial velocity.
$(c)$ The average speed of an object moving with different speeds is the average of those speeds.
$(d)$ The area under the position-time graph represents the displacement of the moving object.

State whether the following statements are true or false:
$(a)$ An object can have acceleration even when its velocity is zero.
$(b)$ If the acceleration of a moving object is constant,the direction of its velocity must remain the same.
$(c)$ The speed of an object can never be zero.