Which graph shows best the velocity-time graph for an object launched vertically into the air when air resistance is given by $| D | = bv?$ The dashed line shows the velocity graph if there were no air resistance.

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$  is proportional to

A bullet of mass $20\,g$ has an initial speed of $1\,ms^{-1}$ just before it starts penetrating a mud wall of thickness $20\,cm.$ If the wall offers a mean resistances of $2.5 \times 10^{-2}\,N,$ the speed of the bullet after emerging from the other side of the wall is close to .............. $\mathrm{ms}^{-1}$

A block of mass $1\,kg$ slides on a rough horizontal surface. If the speed of the block decreases from $10\,m/s$ to $8\,m/s$ , the thermal energy developed in this process .................. $\mathrm{J}$

KE acquired by a mass $m$ in travelling a certain distance $d$, starting from rest, under the action of a constant force $F$ is ..........

$STATEMENT$-$1$ A block of mass $\mathrm{m}$ starts moving on a rough horizontal surface with a velocity $\mathrm{v}$. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of $30^{\circ}$ with the horizontal and the same block is made to go up on the surface with the same initial velocity $v$. The decrease in the mechanical energy in the second situation is smaller than that in the first situation. because

$STATEMENT$- $2$ The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.