Power — Prelims Questions

A pump lifts $200,\text{kg}$ of water through a height of $10,\text{m}$ in $20,\text{s}$. If the efficiency of the pump is $70$, what is the power required by the pump? (Take $g = 10,\text{m/s}^2$)

A constant force of $20,\text{N}$ acts on a body, causing it to move with a constant velocity of $5,\text{m/s}$ in the direction of the force. What is the power delivered by the force?

A motor of power $100,\text{kW}$ is used to lift a mass of $1000,\text{kg}$ to a certain height. If the motor operates for $10,\text{s}$, what is the maximum height the mass can be lifted? (Assume $g = 10,\text{m/s}^2$ and $100$ efficiency)

Which of the following statements about power is INCORRECT?

A particle moves along the x-axis under the action of a force $F = (3x^2 - 2x + 5),\text{N}$. If the particle moves from $x=0$ to $x=2,\text{m}$ in $4,\text{s}$, what is the average power delivered by the force?

A body of mass $m$ is projected vertically upwards with an initial velocity $u$. Neglecting air resistance, what is the instantaneous power delivered by gravity when the body is at its highest point?

An engine pulls a car of mass $1000,\text{kg}$ on a level road at a constant velocity of $10,\text{m/s}$. If the coefficient of friction between the car and the road is $0.1$, what is the power of the engine? (Take $g = 10,\text{m/s}^2$)