An object of mass $2 \,kg$ at rest at origin starts moving under the action of a force $\vec{F}=\left(3 t^2 \hat{i}+4 \hat{j}\right) N$ The velocity of the object at $t=2 \,s$ will be ............. $m / s$

A $6 \,kg$ bomb at rest explodes into three equal pieces $P, Q$ and $R$. If $P$ flies with speed $30 \,m / s$ and $Q$ with speed $40 \,m / s$ making an angle $90^{\circ}$ with the direction of $P$. The angle between the direction of motion of $P$ and $R$ is about

A spacecraft of mass $M$ moves with velocity $V$ in free space at first, then it explodes breaking into two pieces. If after explosion a piece of mass $m$ comes to rest, the other piece of spacecraft will have a velocity

An object of mass $3\,m$ splits into three equal fragments. Two fragments have velocities $v\hat j$ and $v\hat i$. The velocity of the third fragment is

$A$ parallel beam of particles of mass $m$ moving with velocity $v$ impinges on $a$ wall at an angle $\theta$ to its normal . The number of particles per unit volume in the beam is $n$ . If the collision of particles with the wall is elastic, then the pressure exerted by this beam on the wall is :

A shell of mass $m$ moving with velocity $v$ suddenly breaks into $2$ pieces. The part having mass $m/3$ remains stationary. The velocity of other part will be