The position vector of a particle is given as $\vec{r} = (t^2 - 8t + 12)\hat{i} + t^2\hat{j}$. The time after which the velocity vector and acceleration vector become perpendicular to each other is equal to ........ $sec$.

$A$ small block is shot into each of the four tracks as shown below. Each of the tracks rises to the same height. The speed with which the block enters the track is the same in all cases. At the highest point of the track,the normal reaction is maximum in

Will the linear velocity of a particle rotating with a constant angular speed about a non-fixed axis be constant? Why?

$A$ charged particle of mass $m = 2 \ kg$ and charge $q = 1 \ \mu C$ is projected from a horizontal ground at an angle $\theta = 45^{\circ}$ with speed $u = 10 \ ms^{-1}$. In space,a horizontal electric field $E = 2 \times 10^7 \ NC^{-1}$ exists in the direction of projection. The range of the projectile is......$m$.

An aircraft is flying at a height of $H$ above the ground at a constant speed $V$. What is the maximum angle subtended at a ground observation point by the aircraft's path after time $T$?

If $T$ is the total time of flight,$h$ is the maximum height,and $R$ is the horizontal range,how are the $x$ and $y$ coordinates of projectile motion related to time $t$ and range $R$?