The trajectory of a particle moving in a plane is as shown in the figure. The coordinates of position $A$ are $(0, 2)$. The coordinates of another point at which the instantaneous velocity is the same as the average velocity between the points $(0, 2)$ and $(5, 3)$ are:

$A$ particle is moving in the $xy$-plane such that its position coordinates are given by $x = (4t + t^2) \text{ m}$ and $y = (2t + \frac{t^2}{2}) \text{ m}$,where $t$ is in seconds. What is the velocity of the particle?

$A$ particle starts from the origin at $t=0$ with a velocity $5.0 \hat{i} \; m/s$ and moves in the $x-y$ plane under the action of a force which produces a constant acceleration of $(3.0 \hat{i} + 2.0 \hat{j}) \; m/s^2$.
$(a)$ What is the $y$-coordinate of the particle at the instant its $x$-coordinate is $84 \; m$?
$(b)$ What is the speed of the particle at this time?

The position of a particle moving in the $xy$-plane at any time $t$ is given by $x = (3t^2 - 6t) \text{ m}$ and $y = (t^2 - 2t) \text{ m}$. Select the correct statement about the moving particle from the following:

$A$ particle starts from the origin at $t=0$ with a velocity of $10 \hat{j} \text{ ms}^{-1}$ and moves in the $x-y$ plane with a constant acceleration of $(8 \hat{i} + 2 \hat{j}) \text{ ms}^{-2}$. At an instant when the $x$-coordinate of the particle is $16 \text{ m}$, the $y$-coordinate of the particle is: (in $\text{ m}$)

The position vector of a moving body at any instant of time is given as $\overrightarrow{r} = (5t^2 \hat{i} - 5t \hat{j}) \text{ m}$. The magnitude and direction of velocity at $t = 2 \text{ s}$ is,