State the law of conservation of energy.

$A$ boy of mass $40 \, kg$ runs up a flight of $50$ steps,each $10 \, cm$ high,in $5 \, s$. Find: $(i)$ the work done by the boy,and $(ii)$ the power developed. $(g = 9.8 \, m s^{-2})$

$A$ body is moving with constant speed over a frictionless surface. What is the work done by the weight of the body?

$A$ body is thrown vertically upwards. Its velocity goes on decreasing. What is the change in kinetic energy when its velocity becomes zero?

$(a)$ 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?

Justify,giving proper reasoning,whether the work done in the following case is positive or negative: Work done by friction on a body sliding down an inclined plane.