What can be the angle between velocity and acceleration for the motion in two or three dimensions?

$A$ 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?

Explain the position and displacement vectors for a particle moving in a plane using suitable equations.

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 $t=0$ 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?

$A$ point moves in the $x-y$ plane according to $x = kt$ and $y = kt(1 - \alpha t)$,where $k$ and $\alpha$ are positive constants. The equation of the trajectory is: