$A$ block of mass $100 \, g$ moves on a rough surface. The heat produced when its velocity changes from $10 \, m/s$ to $5 \, m/s$ is ....... $J$.

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 .......... $J$.

$A$ ball of mass $1 \ kg$ moves in a straight line with velocity $v = c x^\alpha$, where $c = 1$ ($SI$ unit) and $\alpha$ is a constant. If the work done by the net force during its displacement from $x = 0$ to $x = 4 \ m$ is $128 \ J$, then the value of $\alpha$ is

State the importance of the work-energy theorem. Is the work-energy theorem a scalar or a vector?

$A$ heavy stone is thrown with speed $v$ from a cliff of height $h$. How and in which direction should it be thrown so that the stone hits the ground with maximum speed?

$A$ block of mass $100\, g$ slides on a rough horizontal surface. If the speed of the block decreases from $10\, m/s$ to $5\, m/s,$ the thermal energy developed in the process is............. $J$.