A particle starts from the origin at time \(t=0 \) with an initial velocity of \(5\hat{j}~\text{ms}^{-1}. \) It moves in the \(XY \text-\)plane under a constant acceleration of \(\left(10\hat{i}+4\hat{j}\right)~\text{ms}^{-2} .\) At some later time \(t,\) the coordinates of the particle are \((20~\text{m}, y_0~\text{m}). \) The values of \(t \) and \(y_0 \)​ are, respectively:
1. \(4~\text{s}\) and \(52~\text{m}\)
2. \(5~\text{s}\) and \(25~\text{m}\)
3. \(2~\text{s}\) and \(18~\text{m}\)
4. \(2~\text{s}\) and \(24~\text{m}\)

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 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. \(t^2\sqrt{\alpha^2+\beta^2}~\)

The \(x\) and \(y\) coordinates of the particle at any time are \(x = 5t-2t^2\) and \(y=10t\) respectively, where \(x\) and \(y\) are in metres and \(t\) is in seconds. The acceleration of the particle at \(t=2\) s is:
1. \(0\) m/s²
2. \(5\) m/s²
3. \(-4\) m/s²
4. \(-8\) m/s²