A particle starts from origin at $t=0$ with a velocity $5 \hat{i} \mathrm{~m} / \mathrm{s}$ and moves in $x-y$ plane under action of a force which produces a constant acceleration of $(3 \hat{i}+2 \hat{j}) \mathrm{m} / \mathrm{s}^2$. If the $x$-coordinate of the particle at that instant is $84 \mathrm{~m}$, then the speed of the particle at this time is $\sqrt{\alpha} \mathrm{m} / \mathrm{s}$. The value of $\alpha$ is___________.

The diagram shows the variation of $1 / v$ (where, $v$ is velocity of the particle) with respect to time. At time $t=3\,s$ using the details given in the graph, the instantaneous acceleration will be equal to $...........m/s^{2}$

A target is made of two plates, one of wood and the other of iron. The thickness of the wooden plate is $4\,cm$ and that of iron plate is $2\,cm$. A bullet fired goes through the wood first and then penetrates $1\,cm$ into iron. A similar bullet fired with the same velocity from opposite direction goes through iron first and then penetrates $2\,cm$ into wood. If $a_1$ and $a_2$ be the retardations offered to the bullet by wood and iron plates respectively, then

A body starts from rest from the origin with an acceleration of $6\,m/{s^2}$ along the $x-$axis and $8\,m/{s^2}$ along the $y-$axis. Its distance from the origin after $4 \,seconds$ will be........$m$

A man goes $10\,m $ towards North, then $ 20\,m$ towards east then displacement is........$m$

A person sitting in a moving train with his face towards the engine, throws a coin vertically upwards. The coin falls ahead of person. The train: