The energy required to accelerate a car from $10 \ m/s$ to $20 \ m/s$ is how many times the energy required to accelerate the same car from rest to $10 \ m/s$?

An object of mass $8 \ kg$ moves under the influence of a force. The position of the object varies with time as $x = \frac{1}{2} t^2$,where $x$ is in meters and $t$ is in seconds. Find the work done by the force in the first $2 \ s$ in $J$.

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

Explain the work-energy theorem.

$A$ bullet of mass $0.04\; kg$ moving with a speed of $90\; m/s$ enters a heavy wooden block and is stopped after a distance of $60\; cm$. What is the average resistive force exerted by the block on the bullet (in $; N$)?

$A$ vertical spring with force constant $k$ is fixed on a table. $A$ ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d$. The net work done in the process is