$A$ car of mass $m$ has an engine which can deliver power $P$. The minimum time in which the car can be accelerated from rest to a speed $v$ is .............

$A$ wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed $v$,the electrical power output will be most likely proportional to

$A$ particle of mass $m$ is driven by a machine that delivers a constant power $k$ watts. If the particle starts from rest,the force on the particle at time $t$ is:

$A$ body is moving uni-directionally under the influence of a source of constant power. Its displacement in time $t$ is proportional to

$A$ 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 $m$):

$A$ motor pump lifts $6$ tonnes of water from a well of depth $25 \ m$ to the first floor of height $35 \ m$ from the ground floor in $20$ minutes. The power of the pump (in $kW$) is: $[g=10 \ ms^{-2}]$