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 $x = 3t - 4{t^2} + {t^3}$, where $x$ is in metres and $t$ is in seconds. The work done during the first $4 \,seconds$ is ..... $mJ$

The bob of a pendulum is released from a horizontal position. If the length of the pendulum is $1.\;5 m$, what is the speed (in $m/s$) with which the bob arrives at the lowermost point, given that it dissipated $5\%$ of its initial energy against air resistance ?

An object of mass $m$ is sliding down a hill of arbitrary shape and after traveling a certain horizontal path stops because of friction. The friction coefficient is different for different segments of the entire path but it is independent of the velocity and direction of motion. The work done that a force must perform to return the object  its initial position along the same path would be :-

A cricket ball of mass $0.15\, kg$ is thrown vertically up by a bowling machine so that it rises to a maximum height of $20 \;m$ after leaving the machine. If the part pushing the ball applies a constant force $F$ on the ball and moves horizontally a distance of $0.2\, m$ while launching the ball, the value of $F($ in $N)$ is 

$\left(g=10\, m s^{-2}\right)$

A particle of mass $500 \,gm$ is moving in a straight line with velocity $v=b x^{5 / 2}$. The work done by the net force during its displacement from $x=0$ to $x =4 \,m$ is ...................$J$ (Take $b =0.25 \,m ^{-3 / 2} s ^{-1}$ )

A bungee jumper is jumping with help of elastic ideal rope (Force constant $K$). Jumper steps off the bridge and falls from the rest towards the river below. He does not hit the water. The mass of jumper is $m$, natural length of rope is $l$. Gravity is $g$, assume every thing ideal. then, choose the incorrect option