A particle of mass $m$ slides from rest down a plane inclined at $30^o$ to the horizontal. The force of resistance acting on the particle during motion is $ms^2$ where $s$ is the displacement of the particle from its initial position. The velocity (in $m/s$) of the particle when $s = 1\,m$ is $v$. The value of $\frac{3v^2}{14}$ is :-

Explain the different forms of energy.

$(a)$ Heat Energy

$(b)$ Chemical Energy

$(c)$ Electrical Energy

A ball is thrown vertically downwards from a height of  $20\, m$ with an initial velocity $v_0$, It collides with the ground, loses $50$ percent of its energy in collision and rebounds same height. The initial velocity $v_0$ .................... $\mathrm{ms}^{-2}$ (Take $g=10 \,ms^{-2}$)

A block of mass $1\,kg$ slides on a rough horizontal surface. If the speed of the block decreases from $10\,m/s$ to $8\,m/s$ , the thermal energy developed in this process .................. $\mathrm{J}$

A body of $0.5 \,kg$ moves along the positive $X$-axis under the influence of a varying force $F$ (in newton) as shown below.If the speed of the object at $x=4 \;m$ is $3.16 \,ms ^{-1}$, then its speed at $x=8 \,m$ is ................. $\,ms ^{-1}$

The force constant of a wire is $k$  and that of another wire is $2k.$ When both the wires are stretched through same distance, then the work done