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 the motion is ................ $J$.

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

$A$ car moving with a velocity of $10 \, m/s$ can be stopped by the application of a constant force $F$ in a distance of $20 \, m$. If the velocity of the car is $30 \, m/s$,it can be stopped by this same force in what distance (in $, m$)?

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 $x = \alpha t^2 / 2$, where $x$ is in meters, $t$ is in seconds, and $\alpha = 1 \,m/s^2$. The work done by the force in the first two seconds is: (in $\,J$)

$A$ knife of mass $m$ is dropped from a height $h$ onto a wooden floor. If the blade penetrates a distance $d$ into the wood,what is the average resistance offered by the wood to the knife?

$A$ particle is released from height $S$ above the surface of the earth. At a certain height,its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively: