Calculate the power of an electric motor that can lift $800 \, kg$ of water to store in a tank at a height of $1500 \, cm$ in $20 \, s$. $(g = 10 \, m s^{-2})$ (in $, kW$)

$(a)$ 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 whether the following statement is true or false:
Work done by a force depends upon how fast work is done.

Can any object have mechanical energy even if its momentum is zero? Explain.

The work done in lifting a box onto a platform does not depend upon how fast it is lifted up. Explain your answer giving proper reasoning.

In each of the following cases,a force $F$ is acting on an object of mass $m$. The direction of displacement is from west to east,shown by the longer arrow. Observe the diagrams carefully and state whether the work done by the force is negative $(-ve)$,positive $(+ve)$,or zero $(0)$.