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 .......... .

Let $v$ and $a$ denote the velocity and acceleration respectively of a body. Which of the following statements is correct?

$A$ particle moving in a straight line covers half the distance with speed $6 \, m/s$. The other half is covered in two equal time intervals with speeds $9 \, m/s$ and $15 \, m/s$ respectively. The average speed of the particle during the motion is: (in $ \, m/s$)

$A$ particle moves along the sides $AB, BC, CD$ of a square of side $25 \, m$ with a constant velocity of $15 \, m \, s^{-1}$. Its average velocity is ........ $m \, s^{-1}$.

$A$ train starting from rest first accelerates uniformly up to a speed of $80 \ km/h$ for time $t$,then it moves with a constant speed for time $3t$. The average speed of the train for this duration of journey will be (in $km/h$):

Select the incorrect statement among the following$:-$
$S_1 :$ If the acceleration is zero,a moving particle will perform uniform motion.
$S_2 :$ Motion with constant speed may or may not be uniform motion.
$S_3 :$ If a particle moves on a curved path,its acceleration can never be zero.
$S_4 :$ In successive time intervals,if the average velocities of a particle are equal,then the particle must be moving with uniform velocity.