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Q. No.A particle is moving such that its position coordinates \((x,y)\) are \( (2~\text m, 3~\text m)\) at time \(t=0,\) \( (6~\text m, 7~\text m)\) at time \(t=2~\text s\) and \( (13~\text m, 14~\text m)\) at time \(t=5~\text s.\) The average velocity vector \((v_{avg})\) from \(t=0\) to \(t=5~\text s\) 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. | \(\frac{11}{5}\left ( \hat{i}+\hat{j} \right )\) |
1. \(4~\text{m/s},\) \(53^\circ\) with \(x\)-axis
2. \(4~\text{m/s},\) \(37^\circ\) with \(x\)-axis
3. \(5~\text{m/s},\) \(53^\circ\) with \(y\)-axis
4. \(5~\text{m/s},\) \(53^\circ\) 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. | The average acceleration must always vanish. |
| 3. | The 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 \(100~\text m,\) taking \(62.8~\text s\) for every circular lap. The average velocity and average speed for each circular lap, respectively, is:
| 1. | \(0,~0\) | 2. | \(0,\) \(10~\text{m/s},\) |
| 3. | \(10~\text{m/s},\) \(10~\text{m/s},\) | 4. | \(10~\text{m/s},\) \(0\) |
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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