List two conditions which need to be satisfied for the work to be done on an object.

$A$ girl of mass $40\, kg$ climbs a rope $6\, m$ long at a constant speed in $15$ seconds. What power does she expend during the climb (in $W$)?

Two bodies of equal masses move with the uniform velocities $v$ and $3v$ respectively. Find the ratio of their kinetic energies.

An automobile engine propels a $1000 \,kg$ car $(A)$ along a levelled road at a speed of $36 \,km \,h^{-1}$. Find the power if the opposing frictional force is $100 \,N$. Now,suppose after travelling a distance of $200 \,m$,this car collides with another stationary car $(B)$ of the same mass and comes to rest. Let its engine also stop at the same time. Now car $(B)$ starts moving on the same level road without its engine started. Find the speed of the car $(B)$ just after the collision.

Define kinetic energy and potential energy. Write an expression for $KE$ of a body of mass $m$ moving with speed $v$. Find the kinetic energy of a stone of $10 \, kg$ moving with a velocity of $10 \, m s^{-1}$.

$A$ rocket is moving up with a velocity $v$. If the velocity of this rocket is suddenly tripled,what will be the ratio of the initial kinetic energy to the final kinetic energy?