$A$ bob of a pendulum of length $0.5 \ m$ has a speed of $6 \ ms^{-1}$ at its lowest point. Find the speed of the bob when the string of the pendulum makes $60^{\circ}$ with the vertical. (Take $g=10 \ ms^{-2}$)

$A$ particle is released from a height $H$. At a certain height,its kinetic energy is half of its potential energy with reference to the surface of the earth. The height and speed of the particle at that instant are respectively:

$A$ block of mass $m$,lying on a smooth horizontal surface,is attached to a spring (of negligible mass) of spring constant $k$. The other end of the spring is fixed,as shown in the figure. The block is initially at rest in an equilibrium position. If now the block is pulled with a constant force $F$,the maximum speed of the block is

$A$ body of mass $M$ is released from a height of $1.5 \ m$ on a curved track. It slides down and moves along a horizontal surface $PQ$ of length $15 \ m$. If the coefficient of friction between the body and the horizontal surface is $0.2$,at what distance from $P$ will the body come to rest (in $m$)?

$A$ particle which is experiencing a force,given by $\vec F = 3\hat i - 12\hat j$,undergoes a displacement of $\vec d = 4\hat i$. If the particle had a kinetic energy of $3\, J$ at the beginning of the displacement,what is its kinetic energy (in $J$) at the end of the displacement?

$A$ particle of mass $m$ moves with a velocity $v = a\sqrt{x}$,where $a$ is a constant and $x$ is the displacement. Find the total work done by all forces during the displacement from $x = 0$ to $x = d$.