An engine pumps water continuously through a hose. Water leaves the hose with a velocity $v$ and $m$ is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water?

$A$ body of mass $2 \text{ kg}$ begins to move under the influence of a time-dependent force $\vec{F} = (2t\hat{i} + 6t^2\hat{j}) \text{ N}$,where $\hat{i}$ and $\hat{j}$ are unit vectors along the $x$ and $y$-axis respectively. The power produced by the force at $t = 2 \text{ s}$ is . . . . . . $\text{W}$.

Two bodies of mass $m_1$ and $m_2$ $(m_2 > m_1)$ are connected by a light inextensible string which passes through a smooth fixed pulley. The instantaneous power delivered by an external agent to pull $m_1$ with constant velocity $v$ is

Assume the aerodynamic drag force on a car is proportional to its speed. If the power output from the engine is doubled,then the maximum speed of the car:

$A$ body moves along a straight line due to a constant power delivered by a machine. The distance covered by the body in time $t$ is proportional to:

$A$ constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time $t$ is proportional to