The coordinates of a moving particle at a time $t$ are given by $x = 5 \sin 10t$ and $y = 5 \cos 10t$. The speed of the particle is:

$A$ projectile is thrown with a velocity of $10\,m/s$ at an angle of $60^{\circ}$ with the horizontal. The time interval between the moments when the speed is $\sqrt{5g}\,m/s$ is $..........\,s$ (take $g=10\,m/s^2$).

The velocities of two particles $A$ and $B$,separated by a distance of $20 \ m$,are as shown in the figure. Find the angular velocity of $B$ with respect to $A$ in $rad/s$.

$A$ wheel of radius $R$ is trapped in a mud pit and spinning. As the wheel is spinning,it splashes mud blobs with initial speed $u$ from various points on its circumference. The maximum height from the centre of the wheel,to which a mud blob can reach is

$A$ particle moves towards east with velocity $5\, m/s$. After $10\, s$,its direction changes towards north with the same velocity. The average acceleration of the particle is

Two stones of masses $m$ and $3m$ are whirled in horizontal circles, the heavier one in a radius $r/3$ and the lighter one in radius $r$. When both the stones experience same centripetal forces, the tangential speed of lighter stone is 'n' times that of the value of heavier stone. The value of 'n' is