The mechanical energy of a freely falling body is......

$A$ car and a truck are moving with the same kinetic energy. If the same retarding force is applied to both by using brakes,what will be the distance traveled by both vehicles before coming to rest?

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 rain drop of mass $1 \text{ g}$, starts with zero velocity from a height of $1 \text{ km}$. It hits the ground with a speed of $5 \text{ m/s}$. The work done by the unknown resistive force is . . . . . . $J$. (take $g = 10 \text{ m/s}^2$)

$A$ chain of length $L$ and mass $m$ is placed upon a smooth surface as shown. The length of the chain on the incline is $b$. Calculate the velocity of the chain when its end reaches point $B$.

The potential energy of a $1 \ kg$ particle free to move along the $x-$axis is given by: $U(x) = (\frac{x^4}{4} - \frac{x^2}{2}) \ J$. The total mechanical energy of the particle is $2 \ J$. Then,the maximum speed (in $m/s$) is: