A block of mass $2 \mathrm{kg}$ moving on a horizontal surface with speed of $4{ \mathrm{m} \mathrm{s}}^{-1}$ enters a rough surface ranging from $x=0.5 \mathrm{m}$ to $x=1.5 \mathrm{m}$. The retarding force in this range of rough surface is related to distance by $F=-kx$ where $k=12 \mathrm{N} {\mathrm{m}}^{-1}$. The speed of the block as it just crosses the rough surface will be 

A car covers $AB$ distance with first one-third at velocity $v_1{ \mathrm{m} \mathrm{s}}^{-1}$, second one-third at $v_2{ \mathrm{m} \mathrm{s}}^{-1}$ and last one-third at $v_3{ \mathrm{m} \mathrm{s}}^{-1}$. If $v_3=3v_1,v_2=2v_1$ and $v_1=11{ \mathrm{m} \mathrm{s}}^{-1}$, then the average velocity of the car is _____ ${ \mathrm{m} \mathrm{s}}^{-1}$.

A person moved from $A$ to $B$ on a circular path as shown in figure. If the distance travelled by him is $60 \mathrm{m}$, then the magnitude of displacement would be : (Given $\cos 135°=-0.7$)