The speed of a particle is doubled,its kinetic energy:

Define: $(a)$ power $(b)$ work done $(c)$ kinetic energy. Give the $SI$ unit of each.

$A$ girl of mass $35 \, kg$ sits on a trolley of mass $5 \, kg$. The trolley is given an initial velocity of $4 \, m \, s^{-1}$ by applying a force. The trolley comes to rest after covering a distance of $16 \, m$. $(a)$ What is the work done on the trolley? $(b)$ What is the work done by the girl?

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

$(a)$ State the law of conservation of energy.
$(b)$ Establish the relation between the $SI$ unit of energy and the commercial unit of energy.
$(c)$ $A$ toy car is displaced through $5 \, m$ on the application of a force of $7 \, N$. Assuming the force acts on the object throughout the displacement,what is the work done in this case?

$A$ ball is dropped from a height of $10 \, m$. If the energy of the ball reduces by $40 \%$ after striking the ground,how much high can the ball bounce back (in $, m$)? $(g = 10 \, m s^{-2})$