The displacement of a particle moving with uniform acceleration in time $t$ is given by $S = 30t + 5t^2$. Its initial velocity is $.......$ (in $m \ s^{-1}$)

The distance travelled by a particle is directly proportional to $t^{1/2}$,where $t =$ time elapsed. What is the nature of motion?

$A$ particle moves along the $x$-axis as $x = 4(t-2) + a(t-2)^2$. Which of the following statements is true?

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 $3 \, s$?

The motion of a particle along a straight line is described by the equation $x = 8 + 12t - t^3$,where $x$ is in meters and $t$ is in seconds. The retardation of the particle when its velocity becomes zero is .......... $m/s^2$.

$A$ particle moving along the $X$-axis has acceleration $f$ at time $t$ given by $f=f_0\left(1-\frac{t}{T}\right)$, where $f_0$ and $T$ are constants. The particle at $t=0$ has zero velocity. In the time interval between $t=0$ and the instant when $f=0$, the particle's velocity is