After on head on elastic collision between two balls of equal masses , one is observed to  have a speed of $3\, m/s$ along positive $x$ -axis and the other has a speed of $2\, m/s$ along negative $x$ -axis. The original velocities of the balls are

Power supplied to a particle of mass $2\, kg$ varies with time as $P = \frac{{3{t^2}}}{2}$ $W$. Here $t$ is in $seconds$ . If velocity of particle at $t = 0$ is $v = 0$. The velocity of particle at time $t = 2\, sec$. will be ........... $\mathrm{m}/ \mathrm{s}$

Three particles of masses $10g, 20g$ and $40g$ are moving with velocities $10\widehat i,10\widehat j$ and  $10\widehat k$ $m/s$ respectively. If due to some mutual interaction, the first particle comes to  rest and the velocity of second particle becomes $\left( {3\widehat i + 4\widehat j\,\,} \right)\, m/s$, then the velocity of third particle is

A body moving with speed $v$ in space explodes into two piece of masses in the ratio $1 : 3.$ If the smaller piece comes to rest, the speed of the other piece is

Curve between net forcevs time is shown Initially particle is at rest .. Which of the following best represents the resulting velocity-time graph of the particle ?

If a spring extends by $x$ on loading then energy stored by the spring is ($T$ is tension in spring, $K$ is spring constant)