In the presence of which of the following is the work-energy theorem valid?

$A$ 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 slides from the top of a smooth hemispherical surface of radius $R$ which is fixed on a horizontal surface. If it separates from the hemisphere at a height $h$ from the horizontal surface,then the speed of the particle is

The velocity-time graph for a body of mass $10 \ kg$ is shown in the figure. The work done on the body in the first two seconds of motion is:

State the importance of the work-energy theorem. Is the work-energy theorem a scalar or a vector?

$A$ force $\overrightarrow{F} = 4 \hat{i} - 15 \hat{j} \text{ N}$ acts on a body, resulting in a displacement of $\overrightarrow{S} = 6 \hat{i} \text{ m}$. If the body had a kinetic energy of $7 \text{ J}$ at the beginning of the displacement, what is the kinetic energy at the end of the displacement (in $\text{ J}$)?