A particle moves along $x$-axis from $x=0$ to $x=5$ metre under the influence of a force $F=7-2 x+3 x^2$. The work done in the process is .............

When the momentum of a body increases by $100\%$, its $KE$ increases by .............. $\%$

A particle fall from height $h$ on $a$ static horizontal plane rebounds. If $e$ is coefficient of  restitution then before coming to rest the total distance travelled during rebounds will  be:-

A particle moves with a velocity $\vec v\, = \,5\hat i - 3\hat j + 6\hat k\,\,m/s$ under the influence of a constant force $\vec F\, = \,10\hat i + 10\hat j + 20\hat k$. Instantaenous power will be ............... $\mathrm{J} / \mathrm{s}$

A $300\ kg$ crate is dropped vertically onto a conveyor belt that is moving at $1.20\ m/s$ . A motor maintains the belt's constant speed. The belt initially slides under the crate, with a coefficient of friction of $0.400$ . After a short time, the crate is moving at the speed of the belt. During the period in which the crate is being accelerated, find the work done by the motor which drives the belt ................... $\mathrm{J}$

A particle is made to move from the origin in three spells of equal distances, first along the $x-$ axis, second parallel to $y-$ axis and third parallel to $z-$ axis. One of the forces acting on it is has constant magnitude of $50\,N$ and always acts along the direction of motion. Work done by this force in the three spells of motion are equal and total work done in all the three spells is $300\,J$. The final coordinates of the particle will be