The velocity-time graph for a body of mass $10 \ kg$ is shown in the figure. The work done on the body in the first two seconds of motion is:

Under the action of a force,a $2 \, kg$ body moves such that its position $x$ as a function of time $t$ is given by $x = \frac{t^2}{3}$,where $x$ is in metres and $t$ is in seconds. The work done by the force in the first two seconds is .......... $J$.

$A$ uniform chain of length $3\, m$ and mass $3\, kg$ overhangs a smooth table with $2\, m$ laying on the table. If $k$ is the kinetic energy of the chain in joules as it completely slips off the table,then the value of $k$ is (Take $g = 10\, m/s^2$).

Derive the work-energy theorem for a variable force exerted on a body in one dimension.

State the principle of conservation of mechanical energy for a conservative force.

$A$ particle of mass $100 \ g$ is thrown vertically upwards with a speed of $5 \ m/s$. The work done by the force of gravity during the time the particle goes up is.....$J$