Power

A bus of mass $5$ metric tonne is pulled at a speed of $18 \mathrm{km} {\mathrm{h}}^{-1}$ on a smooth inclination $1$ in $10$. Power of the engine is

The power output from a certain experimental car which is designed in shape like a cube is proportional to the mass $m$ of the car. The force of air friction on the car is proportional to $A{v}^2$, where $v$ is the speed of the car and $A$ the cross sectional area. On a level surface the car has a maximum speed $v_{\max }$. Assuming that all geometrically similar versions of this design have the same density, then which of the following is true?

What will be the power delivered by all the forces acting on the bob of a pendulum when it is making angle $30°$ with the verticle? If it is released from a position where it makes an angle $60°$ with the verticle from rest. The mass of the bob is $1 \mathrm{kg}$ and length is $1 \mathrm{m}$. ($g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

An engine pumps up $1000 \mathrm{kg}$ of coal from a mine $100 \mathrm{m}$ deep in $0.5 \sec$. The pump is running with diesel and efficiency of diesel engine is $25\%$. Then its power consumption will be $\left(g=10 \mathrm{m} {\sec }^{-2}\right)$

A block of mass $m$ slides along the horizontal track with kinetic friction $\mu .$ A man pulls the block through a light rope which makes an angle $\mathrm{\theta }$ with the horizontal as shown in the figure. The tension in the light rope is $T$ as shown. The block moves with constant speed $v$. Power delivered by the man to the block is 

A force $\overrightarrow{F}=(3\hat{\mathrm{i}}+4\hat{\mathrm{j}}) \mathrm{N}$ acts on a $2 \mathrm{kg}$ movable object that moves from an initial position $\overrightarrow{d_{\mathrm{i}}}=(-3\hat{\mathrm{i}}-2\hat{\mathrm{j}}) \mathrm{m}$ to a final position $\overrightarrow{d_{\mathrm{f}}}=(5\hat{\mathrm{i}}+4\hat{\mathrm{j}}) \mathrm{m}$ in $6 \mathrm{s}$. The average power delivered by the force during the interval is equal to

An elevator can carry a maximum load of $1000 \mathrm{kg}$ is moving up with a constant speed of $2 \mathrm{m} {\mathrm{s}}^{-1}$. The frictional force opposing the motion is $2000 \mathrm{N}$. The minimum power delivered by the motor to the elevator is (Assuming $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

The position $\left(x\right)$ of a body moving along x-axis at time $\left(t\right)$ is given by $\mathrm{x}=3{\mathrm{t}}^2,$where $x$ is in metre and $t$ is in second. If mass of body is $2 \mathrm{kg},$ then find the instantaneous power delivered to body by force acting on it at $t=4 \mathrm{s} :-$

Which one of the following is not the unit of energy?

what is the relation between horsepower and watt?

How are Joule (J) and ergs (erg) related?

How much energy does a 100w electric bulb produce in 1 min?

A block of mass $m$ slides along the track with kinetic friction $\mathrm{\mu }$. A man pulls the block through a rope which makes an angle $\mathrm{\theta }$ with the horizontal as shown in the figure. The block moves with constant speed $v$. Power delivered by man is

What is the power of the engine if it changes the velocity of a  $2.05\times {10}^6 \mathrm{Kg}$ train from $5 \mathrm{m} {\mathrm{s}}^{-1}$ to $25\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$ in $5\mathrm{ }\mathrm{minutes}$ ?

What is the force acting on the particle ? if the kinetic energy K of a particle moving in a straight line depends on the distance s as K = as². 

(where a is a constant)

what is the instantaneous power applied to the particle? if the particle moves with a velocity $\left(5\hat{\mathrm{i}}-3\hat{\mathrm{j}}+6\hat{\mathrm{k}}\right){\text{m s}}^{-1}$ under the influence of a constant force $\overrightarrow{F}=\left(10\hat{\mathrm{i}}-10\hat{\mathrm{j}}+20\hat{\mathrm{k}}\right)\text{N.}$

A particle is moving with a velocity $6\hat{\mathrm{i}}-4\hat{\mathrm{j}}+3\hat{\mathrm{k}} \mathrm{m} {\mathrm{s}}^{-1}$ under the influence of a constant force $\overrightarrow{\mathit{F}}=20\hat{\mathrm{i}}+15\hat{\mathrm{j}}-5\hat{\mathrm{k}} \mathrm{N}$. What will be the instantaneous power applied to the particle.

What is the approximate power delivered to the turbine if water is falling from a height of $100 \mathrm{m}$ at the rate of $100 \mathrm{kg} {\mathrm{s}}^{-1}$? $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

Weight of a person is $800\mathrm{ }\mathrm{N}$. If he runs $4 \mathrm{m}$ on a vertical ladder in $2 \mathrm{s}$ then he needs a power of

The force required to row a boat over the sea is proportional to the square of the speed of the boat. It is found that it takes $24 \mathrm{hp}$ to row a certain boat at a speed of $8 \mathrm{k}\mathrm{m} {\mathrm{hr}}^{-1}$, the horsepower required when speed is doubled