Power supplied to a particle of mass $2\, kg$ varies with time as $P = \frac{{3{t^2}}}{2}$ $watt$ . Here, $t$ is in $seconds$ . If velocity of particle at $t = 0$ is $v = 0$, the velocity of particle at time $t = 2s$ will be ............. $\mathrm{m}/ \mathrm{s}$
$1$
$4$
$2$
$2\sqrt 2$
A bullet of mass $m$ moving with a speed $v$ strikes a wooden block of mass $M$ and gets embedded into the block. The final speed is
A bullet of mass $m$ moving with velocity $v$ strikes a suspended wooden block of mass $M$. If the block rises to a height $h$, the initial velocity of the bullet will be
$A$ ball is dropped from $a$ height $h$. As it bounces off the floor, its speed is $80$ percent of what it was just before it hit the floor. The ball will then rise to $a$ height of most nearly .............. $\mathrm{h}$
A basket and its contents have mass $M$. A monkey of mass $2M$ grabs the other end of the rope and very quickly (almost instantaneously) accelerates by pulling hard on the rope until he is moving with a constant speed of $v_{m/r} = 2ft/s$ measured relative to the rope. The monkey then continues climbing at this constant rate relative to the rope for $3$ seconds. How fast is the basket rising at the end of the $3$ seconds? Neglect the mass of the pulley and the rope. (given : $g = 32ft/s^2$)
Power applied to a particle varies with time as $P = (4t^3 -5t + 2)\,watt$, where $t$ is in second. Find the change is its $K.E.$ between time $t = 2$ and $t = 4 \,sec.$ ............... $\mathrm{J}$