The coordinates of a particle moving in the $x-y$ plane are given by: $x = 2 + 4t$,$y = 3t + 8t^2$. The motion of the particle is:

$A$ particle is moving in $x-y$ plane according to $\vec{r} = b \cos \omega t \hat{i} + b \sin \omega t \hat{j}$,where $\omega$ is a constant. Which of the following statement$(s)$ is/are true?

$A$ body of mass $2 \; kg$ has an initial velocity of $3 \; m/s$ along $OE$ and it is subjected to a force of $4 \; N$ in the $OF$ direction,which is perpendicular to $OE$. The displacement of the body from $O$ after $4 \; s$ will be: (in $; m$)

$A$ projectile is fired from the surface of the earth with a velocity of $5 \, m s^{-1}$ and angle $\theta$ with the horizontal. Another projectile is fired from another planet with a velocity of $3 \, m s^{-1}$ at the same angle and follows a trajectory which is identical to the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in $m s^{-2}$) (Given $g = 9.8 \, m s^{-2}$):

$A$ ball is projected at an angle of $45^{\circ}$ with the horizontal. It passes through a wall of height $h$ at a horizontal distance $d_1$ from the point of projection and strikes the ground at a distance $d_1+d_2$ from the point of projection. Then $h$ is:

The figure shows the $(x, t)$ and $(y, t)$ diagrams of a particle moving in $2$ dimensions. If the particle has a mass of $500 \, g$,find the force (magnitude and direction) acting on the particle.