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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. | \(\frac{11}{5}\left ( \hat{i}+\hat{j} \right )\) |
\(\vec{r}=(3.0t\hat{i}-2.0t^{2}\hat{j}+4.0\hat{k})\) 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
In a two-dimensional motion, instantaneous speed \(v_0\) is a positive constant. Then which of the following is necessarily true?
| 1. | the average velocity is not zero at any time. |
| 2. | average acceleration must always vanish. |
| 3. | displacements in equal time intervals are equal. |
| 4. | equal path lengths are traversed in equal intervals. |
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, \(0\) |
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. \(2\sqrt{10}~\text{unit}\)
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Q. No.
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