$A$ body of mass $m$ is moving with uniform acceleration such that at time $t_1$ its velocity is $v$. What is the work done on the body at any time $t$?

The system shown in the figure is released from rest. The pulley and spring are massless,and friction is absent everywhere. The speed of the $5 \, kg$ block when the $2 \, kg$ block leaves contact with the ground is (take the force constant of the spring $k = 40 \, N/m$ and $g = 10 \, m/s^2$):

$A$ 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 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:

$A$ force acts on a $3\, g$ particle in such a way that the position of the particle as a function of time is given by $x = 3t - 4t^2 + t^3$,where $x$ is in $meters$ and $t$ is in $seconds$. The work done during the first $4\, seconds$ is ................. $mJ$.

$A$ 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