$A$ 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 . . . . . . $m/s^2$.

$A$ body starting from rest moves with constant acceleration. The ratio of distance covered by the body during the $5^{th}$ second to that covered in $5$ seconds is

$A$ particle moving along the $x-$axis has acceleration $f$ at time $t$,given by $f = f_0(1 - t/T)$,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 $(v_x)$ is:

The acceleration of an object increases with time as $a = bt$. The object starts from the origin with an initial velocity $v_0$. Find the distance traveled by the object in time $t$.

An object is moving with a uniform acceleration which is parallel to its instantaneous direction of motion. The displacement $(s)-$ velocity $(v)$ graph of this object is

$A$ particle is moving in a straight line with initial velocity $u$ and uniform acceleration $a$. If the sum of the distance travelled in the $t^{\text{th}}$ and $(t+1)^{\text{th}}$ seconds is $100 \text{ cm}$,then its velocity after $t$ seconds,in $\text{cm/s}$,is: