What does $\dot x$ represent?

The relation $3t = \sqrt{3x} + 6$ describes the displacement of a particle in one direction,where $x$ is in $m$ and $t$ is in $s$. The displacement,when velocity is zero,is ......... $m$.

$A$ ball is thrown vertically upwards. Which of the following graphs represents the velocity-time graph of the ball during its flight (air resistance is neglected)?

The graph of displacement $s$ versus time $t$ is given below. Its corresponding velocity-time graph will be:

$A$ car starts from rest and travels with uniform acceleration $\alpha$ for some time and then with uniform retardation $\beta$ and comes to rest. If the total travel time of the car is $t$,the maximum velocity attained by it is given by:

$A$ train starting from rest travels the first part of its journey with constant acceleration $a$,the second part with constant velocity $v$,and the third part with constant retardation $a$,finally being brought to rest. The average speed for the whole journey is $\frac{7v}{8}$. The train travels with constant velocity for what fraction of the total time?