$A$ block of mass $5 \, kg$ is moving with a horizontal velocity of $1.5 \, m/s$. $A$ force of $5 \, N$ is applied in the perpendicular (vertical) direction for $4 \, s$. The total distance covered by the block is .......... $m$.

$A$ boy ties a stone of mass $100 \,g$ to the end of a $2 \,m$ long string and whirls it around in a horizontal plane. The string can withstand a maximum tension of $80 \,N$. If the maximum speed with which the stone can revolve is $\frac{K}{\pi} \,rev/min$,find the value of $K$. (Assume the string is massless and unstretchable)

$A$ body is projected with velocity $u$ making an angle $\alpha$ with the horizontal. Its velocity when it is perpendicular to the initial velocity vector $u$ is

$A$ particle of mass $m$ moves with constant speed $v$ on a circular path of radius $r$ as shown in the figure. The average force on it during its motion from $A$ to $B$ is

$A$ strap is passing over a wheel of radius $30\, cm.$ During the time the wheel moving with an initial constant velocity of $2\, rev/s$ comes to rest,the strap covers a distance of $25\, m.$ The deceleration of the wheel in $rad/s^2$ is

$A$ body $P$ is projected at an angle of $30^{\circ}$ with the horizontal and another body $Q$ is projected at an angle of $30^{\circ}$ with the vertical. If the ratio of the horizontal ranges of the bodies $P$ and $Q$ is $1: 2$, then the ratio of the maximum heights reached by the bodies $P$ and $Q$ is