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Q. No.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:
| 1. | \(\frac{1}{5}\left ( 13\hat{i}+14\hat{j} \right )\) | 2. | \(\frac{7}{3}\left ( \hat{i}+\hat{j} \right )\) |
| 3. | \(2\left ( \hat{i}+\hat{j} \right )\) | 4. | \(\frac{11}{5}\left ( \hat{i}+\hat{j} \right )\) |
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:
| 1. | \(0,~0\) | 2. | \(0,~10\) m/s |
| 3. | \(10\) m/s, \(10\) m/s | 4. | \(10\) m/s, \(0\) |
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. | \(t^{2} \sqrt{\alpha^{2} +\beta^{2}}\) |
Two particles \(A\) and \(B\), move with constant velocities \(\overrightarrow{v_1}\) and \(\overrightarrow{v_2}\). At the initial moment their position vector are \(\overrightarrow {r_1}\) and \(\overrightarrow {r_2}\) respectively. The condition for particles \(A\) and \(B\) for their collision to happen will be:
| 1. | \(\overrightarrow{r_{1 }} . \overrightarrow{v_{1}} = \overrightarrow{r_{2 }} . \overrightarrow{v_{2}}\) | 2. | \(\overrightarrow{r_{1}} \times\overrightarrow{v_{1}} = \overrightarrow{r_{2}} \times \overrightarrow {v_{2}}\) |
| 3. | \(\overrightarrow{r_{1}}-\overrightarrow{r_{2}}=\overrightarrow{v_{1}} - \overrightarrow{v_{2}}\) | 4. | \(\frac{\overrightarrow{r_{1}} - \overrightarrow{r_{2}}}{\left|\overrightarrow{r_{1}} - \overrightarrow{r_{2}}\right|} = \frac{\overrightarrow{v_{2}} - \overrightarrow{v_{1}}}{\left|\overrightarrow{v_{2}} - \overrightarrow{v_{1}}\right|}\) |
Two particles move from \(A\) to \(C\) and \(A\) to \(D\) on a circle of radius \(R\) and diameter \(AB\). If the time taken by both particles are the same, then the ratio of magnitudes of their average velocities is:
1. \(2\)
2. \(2\sqrt{3}\)
3. \(\sqrt{3}\)
4. \(\dfrac{\sqrt{3}}{2}\)
\(\vec{r}=(3.0t\hat{i}-2.0t^{2}\hat{j}+4.0\hat{k})\) m where \(t\) is in seconds and the coefficients have the proper units for \(r\) to be in metres. The magnitude and direction of \(\vec{v}(t)\) at\(t=1.0\) s are:
1. \(4\)m/s,\(53^\circ\) with \(x\)-axis
2. \(4\) m/s, \(37^\circ\) with \(x\)-axis
3. \(5\) m/s,\(53^\circ\) with \(y\)-axis
4. \(5\)m/s, \(53^\circ\) with \(x\)-axis
A bus is going to the North at a speed of \(30\) kmph. It makes a \(90^{\circ}\) left turn without changing the speed. The change in the velocity of the bus is:
| 1. | \(30\) kmph towards \(W\) |
| 2. | \(30\) kmph towards \(S\text-W\) |
| 3. | \(42.4\) kmph towards \(S\text-W\) |
| 4. | \(42.4\) kmph towards \(N\text-W\) |
Three particles are moving with constant velocities \(v_1 ,v_2\) and \(v\) respectively as given in the figure. After some time, if all the three particles are in the same line, then the relation among \(v_1 ,v_2\) and \(v\) is:
1. \(v =v_1+v_2\)
2. \(v= \sqrt{v_{1} v_{2}}\)
3. \(v = \frac{v_{1} v_{2}}{v_{1} + v_{2}}\)
4. \(v=\frac{\sqrt{2} v_{1} v_{2}}{v_{1} + v_{2}}\)
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Q. No.
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