The figure shows the vertical section of a frictionless surface. $A$ block of mass $2\, kg$ is released from position $A$. Its kinetic energy $(KE)$ as it reaches position $C$ is .............. $J$.

$A$ particle of mass $0.01 \; kg$ travels with velocity given by $4 \hat{i} + 16 \hat{k} \; m s^{-1}$. After some time,its velocity becomes $8 \hat{i} + 20 \hat{j} \; m s^{-1}$. The work done on the particle during this interval of time is ...... $J$.

$A$ box of mass $m$ is released from rest at position $1$ on the frictionless curved track shown. It travels a distance $d$ along the track in time $t$ to reach position $2$,falling a vertical distance $h$. Let $v$ be the instantaneous speed and $a$ be the instantaneous acceleration of the box at position $2$. Which of the following equations is valid for this situation?

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 $g = 10 \, m/s^2$):

The bob of a pendulum was released from a horizontal position. The length of the pendulum is $10 \ m$. If it dissipates $10 \%$ of its initial energy against air resistance,the speed with which the bob arrives at the lowest point is : [Use $g = 10 \ ms^{-2}$]

Brakes stop a train in a distance $x$. If the braking force is reduced to one-fourth of its original value,what distance will the train travel before coming to a stop?