The power of a motor pump is $2 \, kW$. How much water per minute can the pump raise to a height of $10 \, m$ (in $kg$)? (Given $g = 10 \, m \, s^{-2}$)

Identify the energy possessed by a rolling stone.

$(a)$ Derive an expression for the kinetic energy of a body having mass $m$ and moving with a velocity $v$.
$(b)$ When the velocity of a body is increased $5$ times,what is the change in its kinetic energy?
$(c)$ Two masses $m$ and $2m$ are dropped from heights $h$ and $2h$. On reaching the ground,which will have greater kinetic energy and why?

$A$ rocket is moving up with a velocity $v$. If the velocity of this rocket is suddenly tripled,what will be the ratio of the initial kinetic energy to the final kinetic energy?

$A$ man drops a $10\, kg$ rock from the top of a $5\, m$ ladder. What is its kinetic energy when it reaches the ground? What is its speed just before it hits the ground?

Name at least three commonly used units of energy.