Work Power Energy Questions

The kinetic energies of two similar cars A and B are $100\text{J}$ and $225\text{J}$ respectively. On applying breaks, car A stops after $1000\text{m}$ and car B stops after $1500\text{m}$. If $F_A$ and $F_B$ are the forces applied by the breaks on cars A and B, respectively, then the ratio $F_A/F_B$ is:

A body projected vertically from the earth reaches a height equal to the earth's radius before returning to the earth. The power exerted by the gravitational force is greatest:

The potential energy of a system increases if work is done:

Force $F$ on a particle moving in a straight line varies with distance $d$ as shown in the figure. The work done on the particle during its displacement of $12\text{m}$ is:

Water falls from a height of $60\text{m}$ at the rate of $15\text{kg/s}$ to operate a turbine. The losses due to frictional forces are $10\%$ of the energy. How much power is generated by the turbine? (Take $g=10{\text{m/s}}^2$)

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?

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

A solid cylinder of mass $3\text{kg}$ is rolling on a horizontal surface with velocity $4{\text{ms}}^{-1}$. It collides with a horizontal spring of force constant $200{\text{Nm}}^{-1}$. The maximum compression produced in the spring will be:

A body of mass $1\text{kg}$ begins to move under the action of a time dependent force $\vec{F}=(2t\hat{i}+3t^2\hat{j})\text{N}$, where $\hat{i}$ and $\hat{j}$ are unit vectors along $x$ and $y$ axis. What power will be developed by the force at the time $t$?

A particle of mass $10\text{g}$ moves along a circle of radius $6.4\text{cm}$ with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to $8\times 10^{-4}\text{J}$ by the end of the second revolution after the beginning of the motion?

A bullet of mass $10\text{g}$ moving horizontally with a velocity of $400{\text{ms}}^{-1}$ strikes a wooden block of mass $2\text{kg}$ which is suspended by a light inextensible string of length $5\text{m}$. As a result the centre of gravity of the block is found to rise a vertical distance of $10\text{cm}$. The speed of the bullet after it emerges out horizontally from the block will be:

A particle moves from a point $(-2\hat{i}+5\hat{j})$ to $(4\hat{j}+3\hat{k})$ when a force of $(4\hat{i}+3\hat{j})\text{N}$ is applied. How much work has been done by the force?