Identify the energy possessed by a rolling stone.

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

$(a)$ Define work done by a constant force on an object. Write an expression for the work done.
$(b)$ How much work will be done on an object by a force if the displacement of the object is zero?
$(c)$ What is the kinetic energy of an object? Write an expression for the kinetic energy of an object of mass $m$ moving with a speed $v$.

State the law of conservation of energy.

$(a)$ $A$ person is holding a bucket of water by applying a vertical force of $100 \, N$. He first moves a horizontal distance of $5 \, m$ and then climbs up through stairs a vertical distance of $10 \, m$. Calculate the total work done by the person on the bucket.
$(b)$ Establish the relationship between kinetic energy and momentum of a body.