A particle is moving such that its position coordinates \((x,y)\) are \((2\) m, \(3\) m) at time \(t=0,\)  \((6\) m, \(7\) m) at time \(t=2\) s and   \((13\) m, \(14\) m) at time \(t=5\) s. Average velocity vector \((v_{avg})\) from \(t=0\) to \(t=5\) s is:

The position of a particle is given by; \(\vec{r}=(3.0t\hat{i}-2.0t^{2}\hat{j}+4.0\hat{k})\) m $\stackrel{}{\mathrm{}}$
 where \(t\) is in seconds and the coefficients have the proper units for \(r\) to be in meters. The magnitude and direction of \(\vec{v}(t)\) at \(t=1.0\) s are:

In a two-dimensional motion, instantaneous speed ${\mathrm{v}}_0$ is a positive constant. Then which of the following is necessarily true?

A car turns at a constant speed on a circular track of radius \(100\) m, taking \(62.8\) s for every circular lap. The average velocity and average speed for each circular lap, respectively, is:

If three coordinates of a particle change according to the equations $\mathrm{x}=3{\mathrm{t}}^2,$ $\mathrm{y}=2\mathrm{t},$ $\mathrm{z}=4$, then the magnitude of the velocity of the particle at time \(t=1\) second will be:
1. $2\sqrt{11}$ unit 
2. $\sqrt{34}$ unit
3. \(40\) unit
4. $2\sqrt{10}$ unit