A bullet fired into a fixed target loses half of its velocity after penetrating $1\,cm.$ How much further it will penetrate before coming to rest, assuming that it faces constant resistance to motion

A particle moves a distance $x$ in time $t$ according to equation $x = (t + 5)^{-1}$ The  acceleration of particle is proportional to 

Two trains travelling on the same track are approaching each other with equal speeds of $40\, m/s$. The drivers of the trains begin to decelerate simultaneously when they are just $2.0\, km$ apart. Assuming the decelerations to be uniform and equal, the value of the deceleration to barely avoid collision should be.........$m/{s^2}$

A body starts from rest from the origin with an acceleration of $6\,m/{s^2}$ along the $x-$axis and $8\,m/{s^2}$ along the $y-$axis. Its distance from the origin after $4 \,seconds$ will be........$m$

The velocity of a body depends on time according to the equation $v=\frac{t^2}{10}+20$. The body is undergoing

A body under the action of several forces will have zero acceleration