A force acts on a $2\,kg$ object so that its position is given as a function of time as $x= 3t^2 + 5.$ What is the work done by this force in first $5\,seconds$ ? ................ $\mathrm{J}$

A raindrop of mass $1.00\, g$ falling from a height of $1\,km$ hits the ground with a speed of $50\,m s^{-1}$. Calculate

$(a)$ the loss of $PE$ of the drop

$(b)$ the gain in $KE$ of the drop

$(c)$ Is the gain in $KE$ equal to loss of $PE$ ? If not why ?

Take, $g = 10\, m s^{-2}$.

Explain work energy theorem.

As shown in the figure, a particle of mass $10$ $kg$ is placed at a point $A$. When the particle is slightly displaced to its right, it starts moving and reaches the point $B$. The speed of the particle at $B$ is $x\, m / s$. (Take $\left. g =10\, m / s ^{2}\right)$ The value of $'x'$ to the nearest integer is.........

Explain the different forms of energy.

$(a)$ Heat Energy

$(b)$ Chemical Energy

$(c)$ Electrical Energy

A bullet of mass $20 \,g$ leaves a riffle at an initial speed $100 \,m / s$ and strikes a target at the same level with speed $50 \,m / s$. The amount of work done by the resistance of air will be ......... $J$