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. $\frac{11}{5}$($\hat{i}$+$\hat{j}$)

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:

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