The initial velocity of the particle is $10 \ m/s$ and its retardation is $2 \ m/s^2$. The distance moved by the particle in the $5^{th}$ second of its motion is .......... $m$.

$A$ body moves on a frictionless plane starting from rest. If $S_{n}$ is the distance moved between $t=n-1$ and $t=n$,and $S_{n-1}$ is the distance moved between $t=n-2$ and $t=n-1$,then the ratio $\frac{S_{n-1}}{S_n}$ is $\left(1-\frac{2}{x}\right)$ for $n=10$. The value of $x$ is:

The acceleration $a$ (in $m/s^2$) of a body,starting from rest,varies with time $t$ (in seconds) according to the relation $a = 3t + 4$. The velocity of the body at time $t = 2 \ s$ will be $........ \ m/s$.

The velocity of an object is given by $v = kt$,where $k = 2 \, m/s^2$. What distance (in $m$) will it cover in the first $3 \, s$?

$A$ particle initially at rest starts moving from reference point $x=0$ along the $x$-axis,with velocity $v$ that varies as $v=4 \sqrt{x} \ m/s$. The acceleration of the particle is . . . . . . $m/s^2$.

$A$ student is at a distance of $16 \ m$ from a bus when the bus begins to move with a constant acceleration of $9 \ m \ s^{-2}$. The minimum velocity with which the student should run towards the bus so as to catch it is $\alpha \sqrt{2} \ m \ s^{-1}$. The value of $\alpha$ is