A water pump is used to deliver the water at constant rate. By what factor power of pump should be increased to increase the rates $n$ times?

For a block of mass $m$ to slide without friction up the rise of height $h$ shown, it must have a minimum initial speed of

A simple pendulum consists of a $2.0 \mathrm{kg}$ mass attached to a string. It is released from rest at $x$ as shown. Its speed at the lowest point $y$ is

A block is released from rest at point $P$ and slides along the frictionless track shown. At point $Q,$ its speed is

A ball is held at a height $H$ above a floor. It is then released and falls to the floor. If air resistance can be ignored, which of the five graphs below correctly gives the mechanical energy $E$ of the Earth-ball system as a function of the altitude $y$ of the ball?