Justify,giving proper reasoning,whether the work done in the following case is positive or negative: Work done by gravitational force when a bucket is pulled upwards.

$(a)$ Two bodies have equal masses and are moving with uniform velocities of $2\,v$ and $3\,v$. What is the ratio of their kinetic energies?
$(b)$ $A$ mass is dropped from height $h$. At halfway to the ground,what is the total energy?

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

Calculate the kinetic energy of a car of mass $750 \,kg$ moving with a velocity of $54 \,km \cdot h^{-1}$. Find the new kinetic energy of the car if a passenger of mass $50 \,kg$ sits in the car.

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.

What is the work done by the tension in the string of a simple pendulum?