$A$ force of $(60 \hat{i} + 15 \hat{j} - 3 \hat{k}) \text{ N}$ produces a velocity of $(2 \hat{i} - 4 \hat{j} + 5 \hat{k}) \text{ m/s}$ in a particle. The value of power at that time will be: (in $\text{ W}$)

$A$ motor boat is moving in a river with velocity $\vec{v} = 7 \hat{i} + 2 \hat{j} - 5 \hat{k} \text{ m/s}$. If the flow of water offers a resistive force $\vec{F} = 9 \hat{i} + 3 \hat{j} - 3 \hat{k} \text{ N}$, then the power of the boat is: (in $\text{ W}$)

$A$ quarter horsepower motor runs at a speed of $600 \ rpm$. Assuming $60 \%$ efficiency,the work done by the motor in one rotation is (in $J$)

$A$ $60\; HP$ electric motor lifts an elevator having a maximum total load capacity of $2000\; kg$. If the frictional force on the elevator is $4000\; N$,the speed of the elevator at full load is close to .............. $m/s$.
$(1\; HP = 746\; W, g = 10\; ms^{-2})$

An automobile of mass $m$ accelerates starting from the origin and is initially at rest,while the engine supplies constant power $P$. The position $x$ as a function of time $t$ is given by:

An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of $2\, m/s$. The mass per unit length of water in the pipe is $100\, kg/m$. What is the power of the engine $?$ ................ $W$