The coordinates of a particle moving in the $XY$-plane vary with time as $x = 4t^2$ and $y = 2t$. The locus of the particle is a:

Which two motions are considered to be combined for motion in a plane?

Position of an ant ($S$ in metres) moving in $Y-Z$ plane is given by $S = 2t^2 \hat{j} + 5 \hat{k}$ (where $t$ is in seconds). The magnitude and direction of velocity of the ant at $t = 1 \ s$ will be:

$A$ 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?

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,

The $x$ and $y$ coordinates of a particle at any time $t$ are given by $x = 5t - 2t^2$ and $y = 10t$ respectively,where $x$ and $y$ are in meters and $t$ is in seconds. The acceleration of the particle at $t = 2 \, s$ is . . . . . . $m/s^2$.