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 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

If the position vector of a particle is given by $\vec{r}(t) = (3t)\hat{i} + (4t^2)\hat{j}$,then obtain its velocity vector at $t = 2 \ s$.

An ant is moving on a plane horizontal surface. The number of degrees of freedom of the ant will be .........

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 . . . . . . $m/s^2$.

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,