The coordinates of a moving particle at any time $t$ are given by $x = at^2$ and $y = bt^2$. The speed of the particle at any moment is

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:

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,

$A$ particle moves in the $x-y$ plane with velocity $\vec{v} = a\hat{i} + bx\hat{j}$,where $a$ and $b$ are constants. If the particle was initially at the origin,find the equation of its trajectory.

$A$ particle starts from the origin at $t=0 \; s$ with a velocity of $10.0 \hat{j} \; m/s$ and moves in the $x-y$ plane with a constant acceleration of $(8.0 \hat{i} + 2.0 \hat{j}) \; m/s^2$.
$(a)$ At what time is the $x$-coordinate of the particle $16 \; m$? What is the $y$-coordinate of the particle at that time?
$(b)$ What is the speed of the particle at that time?

Explain average velocity,instantaneous velocity,and components of velocity for motion in a plane.