1. | \(\dfrac{1}{v} = \dfrac{1}{v_1}+\dfrac{1}{v_2}\) | 2. | \(\dfrac{2}{v} = \dfrac{1}{v_1}+\dfrac{1}{v_2}\) |
3. | \(\dfrac{v}{2} = \dfrac{v_1+v_2}{2}\) | 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:
1.
2.
3.
4.
A car moves from \(X\) to \(Y\) with a uniform speed \(v_u\) and returns to \(X\) with a uniform speed \(v_d.\) The average speed for this round trip is:
1. | \(\dfrac{2 v_{d} v_{u}}{v_{d} + v_{u}}\) | 2. | \(\sqrt{v_{u} v_{d}}\) |
3. | \(\dfrac{v_{d} v_{u}}{v_{d} + v_{u}}\) | 4. | \(\dfrac{v_{u} + v_{d}}{2}\) |
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:
\(<v>_{time}\) \(=\) \(\frac{\int v d t}{\int d t}\)
\(<v>_{space}\) \(=\) \(\frac{\int v d s}{\int d s}\)
1. | \(\frac{1}{2}\) | 2. | \(\frac{3}{4}\) |
3. | \(\frac{4}{3}\) | 4. | \(\frac{3}{2}\) |