Initially car $A$ is $10.5 \mathrm{m}$ ahead of car $B$. Both start moving at time $t = 0$ in the same direction along a straight line. The velocity time graph of two cars is shown in figure. Find the time (in $\mathrm{s}$) when the car $B$ will catch the car $A$, will be:

The velocity displacement graph of a particle moving along a straight line is shown.

The most suitable acceleration-displacement graph will be

At $t=0$ second a particle is at point $A$ and moves along the shown path $\left(\mathit{A}\mathit{B}\mathit{C}\mathit{D}\mathit{E}\right)$ with uniform speed $v=\left(1+\frac{\mathrm{\pi }}{3}\right) \mathrm{m} {\mathrm{s}}^{-1}.$ Both the straight segments $AB$ and $DE$ are along the diameter $BD$ of semicircle $BCD$ of radius $R=1$ metre. Then the instant of time at which the instantaneous velocity of the particle is along the direction of average velocity from $t=0 \sec$ to that instant is also

A girl standing at point $P$ on a beach wishes to reach a point $Q$ in the sea as quickly as possible. She can run at $6 \mathrm{km} {\mathrm{h}}^{-1}$ on the beach and swim at $4 \mathrm{km} {\mathrm{h}}^{-1}$ in the sea. She should take the path

Small particle of mass $m$ is projected at an angle $\theta$ with the $x-$axis with an initial velocity $v_0$ in the $x-y$ plane as shown in the figure. At a time $t<\frac{v_0\mathrm{sin\theta }}{g}$ the angular momentum of the particle is

where $\hat{\mathrm{i}}, \hat{\mathrm{j}}$ and $\hat{\mathrm{k}}$ are unit vectors along $x,y$ and $z-$ axis respectively.