A particle of mass $m$ moves along a curve, $y=x^2$. When the particle has $x-$coordinate as $\frac{1}{2} \mathrm{m}$ and $x-$ component of velocity as$4 \mathrm{m} {\mathrm{s}}^{-1}$, then

A ball is projected on smooth inclined plane in direction perpendicular to line of greatest slope with velocity of $8{\mathrm{ms}}^{-1}.$ find it's speed after $1$sec.

Acceleration versus velocity graph of a particle moving in a straight line starting form rest as shown in figure.the corresponding velocity-time graph would be:

An inclined plane makes an angle $30°$ with the horizontal. A groove $OA=5 \mathrm{m}$ cut in the plane makes an angle $30°$ with $OX$. A short smooth cylinder is free to slide down the influence of gravity. The time taken by the cylinder to reach from $A$ to $O$ is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

In the figure shown block $B$ moves down with a velocity $10 \mathrm{m} {\mathrm{s}}^{-1}$. The velocity of $A$ in the position shown is

For shown situation in which interval is the average speed greatest? (Given each interval is of equal duration)