$A$ particle starts from the origin at $t=0$ with an initial velocity of $3.0 \hat{i} \; m/s$ and moves in the $x-y$ plane with a constant acceleration $(6.0 \hat{i} + 4.0 \hat{j}) \; m/s^2$. The $x$-coordinate of the particle at the instant when its $y$-coordinate is $32 \; m$ is $D$ meters. The value of $D$ is

If a body of mass $2 \,kg$ moving with an initial velocity of $4 \,m \,s^{-1}$ is subjected to a force of $3 \,N$ for a time of $2 \,s$ normal to the direction of its initial velocity, then the resultant velocity of the body is

$A$ particle moves in the $xy$-plane with velocity $v_x = 8t - 2$ and $v_y = 2$. If it passes through the point $(14, 4)$ at $t = 2 \, s$,the equation of its path is:

$A$ player kicks a football at an angle of $30^{\circ}$ with the horizontal with an initial speed of $30 \,ms^{-1}$. $A$ second player, standing at a distance of $21 \sqrt{3} \,m$ from the first player in the direction of the kick, starts running to catch the ball at the same instant it is kicked. What is the minimum speed of the second player to catch the ball before it hits the ground? (Take acceleration due to gravity $g = 10 \,ms^{-2}$)

$A$ particle moves over a $xy$ plane with a constant acceleration $\vec{a} = (4.0 \, m \, s^{-2}) \hat{i} + (4.0 \, m \, s^{-2}) \hat{j}$. At time $t = 0$,the velocity is $\vec{v}_0 = (4.0 \, m \, s^{-1}) \hat{i}$. The speed of the particle when it is displaced by $6.0 \, m$ parallel to the $x$-axis is,

$A$ fighter plane flying horizontally at an altitude of $1.5 \; km$ with a speed of $720 \; km/h$ passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell with a muzzle speed of $600 \; m s^{-1}$ to hit the plane? At what minimum altitude should the pilot fly the plane to avoid being hit? (Take $g = 10 \; m s^{-2}$).