State the importance of work energy theorem. Whether the work energy theorem is a scalar or a vector ?
$(1)$ If the change in kinetic energy $\Delta K$ of a body is zero, then the work done on the body is zero and its kinetic energy remains constant and hence the speed of the body remains constant.
For example : the speed of a particle in uniform circular motion is constant and work done is zero.
$(2)$ If the displacement of a body is in the same direction of force or displacement is in direction of component of force then the work done on the body and hence the kinetic energy of body increases.
For example, free fall body.
$(3)$ If the displacement of a body is opposite in the direction of force or displacement is in the opposite direction of component of force then the work done by the body and hence, the kinetic energy of body decreases.
A small steel sphere of mass $m$ is falling vertically through a viscous liquid with a constant speed $v$ . Which row in the table correctly describes the changes with time in the kinetic energy and gravitational potential energy of the sphere?
Kinetic Energy || Gravitational Potential Energy
$A$ box of mass $m$ is released from rest at position $1$ on the frictionless curved track shown. It slides a distance $d$ along the track in time $t$ to reach position $2$, dropping a vertical distance $h$. Let $v$ and $a$ be the instantaneous speed and instantaneous acceleration, respectively, of the box at position $2$. Which of the following equations is valid for this situation?
What is the energy equivalent to one kilogram.
From a building two balls $A$ and $B$ are thrown such that $A$ is thrown upwards and $B$ downwards (both vertically). If $v_{A}$ and $v_{B}$ are their respective velocities on reaching the ground, then
Find the speed of a body at the ground when it fall freely at height $2\,m$. $(g = 10\, ms^{-2})$