A force $\vec F = (5\hat i + 3\hat j)\;N$is applied over a particle which displaces it from its original position to the point $\vec s = (2\hat i - 1\hat j)$m. The work done on the particle is.........$J$

A force acts on a $3\, gm$ particle in such a way that the position of the particle as a function of time is given by $x = 3t -4t^2 + t^3$ , where $x$ is in $meters$ and $t$ is in $seconds$ . The work done during the first $4\, second$ is ................. $\mathrm{mJ}$

A body of mass $m$ is projected from ground with speed $u$ at an angle $\theta$ with horizontal. The power delivered by gravity to it at half of maximum height from ground is

Answer carefully, with reasons :

$(a)$ In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact) ?

$(b)$ Is the total linear momentum conserved during the short time of an elastic collision of two balls ?

$(c)$ What are the answers to $(a)$ and $(b)$ for an inelastic collision ?

$(d)$ If the potential energy of two billiard balls depends only on the separation distance between their centres, is the collision elastic or inelastic ?

(Note, we are talking here of potential energy corresponding to the force during collision, not gravitational potential energy).

A particle moves under the effect of a force $F = cx$ from $x = 0$ to $x = x_1$. The work done in the process is

A block of mass $0.50\, kg$ is moving with a speed of $2.00\, ms^{-1}$ on a smooth surface. It strikes another mass of $1.00\, kg$ and then they move together as a single body. The energy loss during the collision is .............. $\mathrm{J}$