$A$ particle moves along the straight line $y=3x+5$. Which coordinate changes at a faster rate?

Choose the correct statement.

Statement $(I)$: An object subjected to velocities $\overrightarrow{v_1}$ and $\overrightarrow{v_2}$ has a resultant velocity with magnitude $|\vec{v}| = |\overrightarrow{v_1}| + |\overrightarrow{v_2}|$.
Statement $(II)$: The magnitude of displacement is either less than or equal to the path length of an object between two points.
Statement $(III)$: The instantaneous acceleration is the limiting value of the average acceleration as the time interval approaches zero.
Which of the following is correct?

Which one of the following statements is wrong?

$A$ street car moves rectilinearly from station $A$ to the next station $B$ with an acceleration varying according to the law $a = (b - cx)$,where $b$ and $c$ are constants and $x$ is the distance from station $A$. The distance between the two stations and the maximum velocity are:

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 .......... .