Consider the motion of the tip of the minute hand of a clock. In one hour:

Choose the correct option from the given ones:
1. (a) and (b) only
2. (b) and (c) only
3. (c) and (d) only
4. (a) and (d) only

The position of a particle at time \(t\) is given by, \(x=3t^3\), \(y=2t^2+8t\), and \(z=6t-5\). The initial velocity of the particle is:

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 time \(t\) is given by:
1. \(\sqrt{\alpha^2+\beta^2}~\)
2. \(3t\sqrt{\alpha^2+\beta^2}~\)
3. \(3t^2\sqrt{\alpha^2+\beta^2}~\)
4. \(t^2\sqrt{\alpha^2+\beta^2}~\)

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. $\frac{11}{5}$($\hat{i}$+$\hat{j}$)

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 time \(t\) is given by:
1. \(\sqrt{\alpha^2+\beta^2}\)
2. \(3t\sqrt{\alpha^2+\beta^2}\)
3. \(3t^2\sqrt{\alpha^2+\beta^2}\)
4. \(t^2\sqrt{\alpha^2+\beta^2}\)