1. \(3.14~\text{m/s}\)
2. \(2.0~\text{m/s}\)
3. \(1.0~\text{m/s}\)
4. zero

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 a time \(t\) is given by:

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

1. $\frac{1}{5}$(13$\hat{i}$+14$\hat{j}$)

2. $\frac{7}{3}$($\hat{i}$+$\hat{j}$)

3. 2($\hat{i}$+$\hat{j}$)

4. $\frac{11}{5}$($\hat{i}$+$\hat{j}$)

Coordinates of a moving particle are given by $\mathrm{x}={\mathrm{ct}}^2$ and $\mathrm{y}={\mathrm{bt}}^2$. The speed of the particle is given by

(1)  $2\mathrm{t}<mspace\; width="1em"></mspace>\left(\mathrm{c}+\mathrm{b}\right)$

(2)  $2\mathrm{t}<mspace\; width="1em"></mspace>\sqrt{{\mathrm{c}}^2-{\mathrm{b}}^2}$

(3)  $\mathrm{t}<mspace\; width="1em"></mspace>\sqrt{{\mathrm{c}}^2+{\mathrm{b}}^2}$

(4)  $2\mathrm{t}<mspace\; width="1em"></mspace>\sqrt{{\mathrm{c}}^2+{\mathrm{b}}^2}$

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