The force $\vec F\, = F\hat i$ on a particle of mass $2\, kg$, moving along the $x-$ axis is given in the figure as a function of its position $x$. The particle is moving with a velocity of $5\, m/s$ along the $x-$ axis at $x\, = 0$. What is the kinetic energy of the particle at $x\,= 8\, m$ ? .................. $\mathrm{J}$

A shell of mass $200\, gm$ is ejected from a gun of  mass $4\, kg$ by an explosion that generates $1.05\, kJ$ of energy. The initial velocity of the shell is .............. $\mathrm{ms}^{-1}$

A bullet of mass $50 \mathrm{~g}$ is fired with a speed $100 \mathrm{~m} / \mathrm{s}$ on a plywood and emerges with $40 \mathrm{~m} / \mathrm{s}$. The percentage loss of kinetic energy is :

What is the shape of the graph between the speed and kinetic energy of a body

A particle of mass $m_1$ is moving with a velocity $v_1$ and another particle of mass $m_2$ is moving with a velocity $v_2$ . Both of them have the same momentum but their different kinetic energies are $E_1$ and $E_2$ respectively. If $m_1 > m_2$ then

A block moving horizontally on a smooth surface with a speed of $40\, {m} / {s}$ splits into two parts with masses in the ratio of $1: 2$. If the smaller part moves at $60\, {m} / {s}$ in the same direction, then the fractional change in kinetic energy is :-