Water is pumped from a depth of $10 \ m$ and delivered through a pipe of cross-section $10^{-2} \ m^2$. If it is needed to deliver a volume of $10^{-1} \ m^3$ per second,the power required will be ........ $kW$.

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

$A$ car of mass $1250 \ kg$ is moving with a velocity of $30 \ m/s$. If the engine delivers $30 \ kW$ of power and the resistive force acting on the car is $750 \ N$,find the maximum acceleration of the car.

The velocity $v$ reached by a car of mass $m$ at a certain distance from the starting point, driven with constant power $P$, is such that:

$A$ force of $(2\hat i + 3\hat j + 4\hat k) \text{ N}$ acts on a body for $4 \text{ s}$ and produces a displacement of $(3\hat i + 4\hat j + 5\hat k) \text{ m}$. The power used is ............. $\text{W}$. (in $.5$)

An elevator lifts a load of $500 \ kg$ with a constant speed of $0.4 \ m/s$. What is the minimum horsepower $(H.P.)$ of the motor required?