$A$ $2 \, m$ high person is holding a $25 \, kg$ trunk on his head and is standing at a roadways bus-terminus. How much work is done by the person (in $, J$)?

$(a)$ 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?

$A$ body is falling from a height $h$. After it has fallen a height $\frac{h}{2}$,it will possess

How much work should be done on an object of $120 \, kg$ to increase its speed from $25 \, m s^{-1}$ to $40 \, m s^{-1}$ (in $, J$)?

$(a)$ State the law of conservation of energy. Explain it with one example.
$(b)$ Two girls,each of weight $400 \, N$,climb up a rope to a height of $8 \, m$. Girl $A$ takes $20 \, s$ while Girl $B$ takes $50 \, s$ to accomplish the task. What is the power expended by each girl?
$(c)$ An electric heater is rated $1500 \, W$. How much energy does it use in $10 \, h$?

State whether the following statement is true or false:
$A$ force does not work, if it produces no motion.