If a body loses half of its velocity on penetrating $3 \, cm$ in a wooden block,then how much will it penetrate more before coming to rest? (in $cm$)

The distance $x$ covered in time $t$ by a body having initial velocity $u$ and having constant acceleration $a$ is given by $x=ut+\frac{1}{2}at^2$. This result follows from

An object,moving with a speed of $6.25 \ m/s$,is decelerated at a rate given by: $\frac{dv}{dt} = - 2.5\sqrt{v}$,where $v$ is the instantaneous speed. The time taken by the object to come to rest would be ........ $s$.

If the velocity of a particle moving along the $x-$ axis is given by $v = k\sqrt{x}$,then which of the following is true? ($a$ is acceleration)

The velocity of a body moving with a uniform acceleration of $2\,m/s^2$ is $10\,m/s$. Its velocity after an interval of $4\,s$ is...........$m/s$.

Give an example of a motion where $x > 0$,$v < 0$,and $a > 0$ at a particular instant.