A person travelling in a straight line moves with a constant velocity \(v_1\) for a certain distance \(x\) and with a constant velocity \(v_2\) for the next equal distance. The average velocity \(v\) is given by the relation:
1. | \(\frac{1}{v} = \frac{1}{v_1}+\frac{1}{v_2}\) | 2. | \(\frac{2}{v} = \frac{1}{v_1}+\frac{1}{v_2}\) |
3. | \(\frac{v}{2} = \frac{v_1+v_2}{2}\) | 4. | \(v = \sqrt{v_1v_2}\) |
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. The average velocity vector \(\vec{v}_{avg}\) from \(t=\) 0 to \(t=\) \(5\) s is:
1. \({1 \over 5} (13 \hat{i} + 14 \hat{j})\)
2. \({7 \over 3} (\hat{i} + \hat{j})\)
3. \(2 (\hat{i} + \hat{j})\)
4. \({11 \over 5} (\hat{i} + \hat{j})\)
A particle covers half of its total distance with speed ν1 and the rest half distance with speed ν2.
Its average speed during the complete journey is:
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A car moves from \(\mathrm{X}\) to \(\mathrm{Y}\) with a uniform speed \(\mathrm{v_u}\) and returns to \(\mathrm{X}\) with a uniform speed \(\mathrm{v_d}.\) The average speed for this round trip is:
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A particle starts from rest with constant acceleration. The ratio of space-average velocity to the time-average velocity is:
where time-average velocity and space-average velocity, respectively, are defined as follows:
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