$A$ particle is released from height $S$ above the surface of the earth. At a certain height,its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively:

What is the velocity of the bob when it reaches point $B$ in $m/s$?

$A$ toy gun fires a plastic pellet with a mass of $0.5\ g$. The pellet is propelled by a spring with a spring constant of $1.25\ N/cm$, which is compressed $2.0\ cm$ before firing. The plastic pellet travels horizontally $10\ cm$ down the barrel (from its compressed position) with a constant friction force of $0.0475\ N$. What is the speed (in $SI\ units$) of the bullet as it emerges from the barrel?

$A$ particle is released from a height $H$. At a certain height $h$,its kinetic energy is two times its potential energy. The height $h$ and the speed $v$ of the particle at that instant are:

The pulley and spring are massless,and friction is absent everywhere. $A$ $5\, kg$ block is released from rest. Find the speed of the $5\, kg$ block when the $2\, kg$ block leaves contact with the ground. (Take the force constant of the spring $K = 40\, N/m$ and $g = 10\, m/s^2$.)

Potential energy of a body of mass $1 \ kg$ free to move along $X$-axis is given by $U(x) = (\frac{x^2}{2} - x) \ J$. If the total mechanical energy of the body is $2 \ J$,then the maximum speed of the body is (Assume only conservative force acts on the body).