Water falls down a $500.0 \,m$ shaft to reach a turbine which generates electricity. How many $m^3$ of water must fall per second in order to generate $1.00 \times 10^9 \,W$ of power? (Assume $50 \%$ efficiency of conversion and $g=10 \,ms^{-2}$)

$A$ body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time $t$ is proportional to

An elevator can carry a maximum load of $1800 \; kg$ (elevator $+$ passengers) and is moving up with a constant speed of $2 \; m s^{-1}$. The frictional force opposing the motion is $4000 \; N$. Determine the minimum power delivered by the motor to the elevator in watts as well as in horsepower.

An electric motor produces a tension of $4500 N$ in a wire and the reel winds at a rate of $2 ms^{-1}$. What is the power of the electric motor?

$A$ body of mass $2\, kg$ is driven by an engine delivering a constant power $1\, J/s$. The body starts from rest and moves in a straight line. After $9$ seconds,the body has moved a distance (in $m$):

An electric motor exerts a force of $40 N$ on a cable and pulls it by a distance of $30 m$ in one minute. The power supplied by the motor (in Watts) is