$A$ body is moving with constant speed over a frictionless surface. What is the work done by the weight of the body?

When is the work done by a force said to be negative? Give one situation in which one of the forces acting on the object is doing positive work and the other is doing negative work.

Two children $A$ and $B$ each weighing $20 \, kg$ climb a rope up to a height of $10 \, m$. Child $A$ takes $10 \, s$ and child $B$ takes $20 \, s$ to climb. State whether the work done by both is equal or unequal. Who has more power?

$(i)$ An object thrown at a certain angle to the ground moves in a curved path and falls back to the ground. The initial and the final points of the path of the object lie on the same horizontal line. What is the total work done against the force of gravity and by the force of gravity on the object? Explain with proper mathematical expression.
$(ii)$ $A$ certain force acting on a $20 \, kg$ mass changes its velocity from $5 \, m s^{-1}$ to $2 \, m s^{-1}$. Calculate the work done by the force.

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 $, kW$)

$(a)$ $A$ 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.