The same retarding force is applied to stop a train. The train stops after $80 m$. If the speed is doubled, then the distance will be

A particle of mass $0.1 \,kg$ is subjected to a force which varies with distance as shown. If it starts its journey from rest at $x=0$, then its velocity at $x=12 \,m$ is .............. $m / s$

If the kinetic energy of a body is directly proportional to time $t,$ the magnitude of force acting on the body is

$(i)$ directly proportional to $\sqrt t$
$(ii)$  inversely proportional to  $\sqrt t$
$(iii)$ directly proportional to the speed of the body
$(iv)$ inversely proportional to the speed of body

A $50\,kg$ man with $20\,kg$ load on his head climbs up $20$ steps of $0.25\,m$ height each. The work done in climbing is......$J$

Define kinetic energy. Give its unit and dimensional formula and mention works by using it.

Two bodies of masses $m$ and $4 \,m$ are moving with equal $K.E.$ The ratio of their linear momentums is