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:

Explain average acceleration and instantaneous acceleration.

The position vector of a particle changes with time according to the relation $\vec{r}(t) = 15t^2 \hat{i} + (4 - 20t^2) \hat{j}$. What is the magnitude of the acceleration at $t = 1 \ s$?

Write the equations of motion for uniformly accelerated motion in a plane.

The magnitude of acceleration and velocity of a particle moving in a plane,whose position vector is $\vec{r} = 3t^2 \hat{i} + 2t \hat{j} + \hat{k}$ at $t = 2 \text{ s}$,are,respectively:

$A$ 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 $\text{ m}$)