$A$ 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:

$A$ 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 ....... $s$.

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.

$A$ particle starts from rest,accelerates at $2 \, m/s^2$ for $10 \, s$,then moves at a constant speed for $30 \, s$,and finally decelerates at $4 \, m/s^2$ until it stops. What is the total distance travelled by it in $m$?

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

$A$ car travels from $A$ to $B$ (without changing direction). During the first part of the journey,its average speed is $V_1$,and for the second part of the journey,its average speed is $V_2$. The ratio of the path length of the second part to the path length of the first part is $\sqrt{\frac{V_2}{V_1}}$. In this case,the average speed of the total path is the ....... of the average speeds of both parts. Choose the correct option.