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Q. No.A person travelling on a straight line moves with a uniform velocity \(v_1,\) for some time and with uniform velocity \(v_2\) for the next equal time. The average velocity \(v\) is given by:
1. \(v=\frac{v_{1}+v_{2}}{2}\)
2. \(v=\sqrt{v_{1} v_{2}}\)
3. \(\frac{2}{v}=\frac{1}{v_{1}}+\frac{1}{v_{2}}\)
4. \(\frac{1}{v}=\frac{1}{v_{1}}+\frac{1}{v_{2}}\)
A person traveling on a straight line moves with a uniform velocity \(v_1\) for a distance \(x\) and with a uniform velocity \(v_2,\) for the next equal distance. The average velocity \(v\) is given by:
1. \(v=\frac{v_{1}+v_{2}}{2}\)
2. \(v=\sqrt{v_{1} v_{2}}\)
3. \(\frac{2}{v}=\frac{1}{v_{1}}+\frac{1}{v_{2}}\)
4. \(\frac{1}{v}=\frac{1}{v_{1}}+\frac{1}{v_{2}}\)
Pick the correct statements:
| a. | Average speed of a particle in a given time is never less than the magnitude of the average velocity. |
| b. | It is possible to have a situation in which \(|\frac{d \vec{v}}{d t}| \neq 0\) but \(\frac{d}{d t}|\vec{v}|=0.\) |
| c. | The average velocity of a particle is zero in a time interval. It is possible that the instantaneous velocity is never zero in the interval. |
| d. | The average velocity of a particle moving in a straight line is zero in a time interval. It is possible that the instantaneous velocity is never zero in the interval. (Infinite accelerations are not allowed) |
Choose the correct option:
| 1. | (a), (b) and (c) |
| 2. | (b), (c) and (d) |
| 3. | (a) and (b) |
| 4. | (b) and (c) |
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