$A$ hall has the dimensions $10\,m \times 12\,m \times 14\,m$. $A$ fly starting at one corner ends up at a diametrically opposite corner. What is the magnitude of its displacement in meters?

The coordinates of a moving particle at any time $t$ are given by $x = \alpha t^3$ and $y = \beta t^3$. The speed of the particle at time $t$ is given by

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

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 $t = 1 \ s$?

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 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?