$A$ ball moves one-fourth of a circle of radius $R$ in time $T$. Let $v_1$ and $v_2$ be the magnitudes of mean speed and mean velocity vector. The ratio $\frac{v_1}{v_2}$ will be

Two particles $P$ and $Q$ simultaneously start moving from point $A$ with velocities $15\,m/s$ and $20\,m/s$ respectively. The two particles move with accelerations equal in magnitude but opposite in direction. When $P$ overtakes $Q$ at $B$,then its velocity is $30\,m/s$. The velocity of $Q$ at point $B$ will be $..........\,m/s$.

Two stones are thrown up vertically and simultaneously but with different speeds. Which graph correctly represents the time variation of their relative position $\Delta x$? Assume that stones do not bounce after hitting the ground.

$A$ body of mass $m$ moving along a straight line covers half the distance with a speed of $2 \,ms^{-1}$. The remaining half of the distance is covered in two equal time intervals with a speed of $3 \,ms^{-1}$ and $5 \,ms^{-1}$ respectively. The average speed of the particle for the entire journey is

The displacement $x$ of a particle depends on time $t$ as $x = \alpha t^2 - \beta t^3$.

$A$ bead is moving in medium $1$ with a uniform speed of $1\, m/s$ for $2.5\, s$. Then it enters into air and falls freely under gravity for $2\, m$. Finally, it enters medium $2$ and immediately moves with uniform speed for $1.5\, s$. The total distance the bead has traveled is.........$m$ $(g = 10\, m/s^2)$: (in $.1$)