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 $t = 4 \,sec.$ ............... $\mathrm{J}$

In an elastic collision of two particles the following quantity is conserved

A cord is used to lower vertically a block of mass $M$ by a distance $d$ with constant downward acceleration $\frac{g}{4}$. Work done by the cord on the block is

A long spring, when stretched by a distance $x,$ has the potential energy $u.$ On increasing the stretching to $nx.$ The potential energy of the spring 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 particle moves with a velocity $\vec v\, = \,5\hat i - 3\hat j + 6\hat k\,\,m/s$ under the influence of a constant force $\vec F\, = \,10\hat i + 10\hat j + 20\hat k$. Instantaenous power will be ............... $\mathrm{J} / \mathrm{s}$