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Q. No.A particle moves around a circle with a unique uniform speed in each revolution. After the first revolution and during the \(2\)nd revolution: its speed doubles; and during the \(3\)rd revolution, its speed becomes \(3\) times the initial speed and so on. The time for the \(1\)st revolution is \(12\) sec. The average time per revolution, for the first four revolutions, is:
1. \(4.8\) s
2. \(9.6\) s
3. \(6.25\) s
4. \(6\) s
Subtopic: Â Average Speed & Average Velocity |
 69%
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Given below are two statements:
| Assertion (A): | The average speed of a particle that has undergone motion can be zero, but its average acceleration cannot be zero. |
| Reason (R): | The average speed is the distance travelled per unit time over the entire motion, while the average acceleration is the change in velocity divided by the time. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Â Average Speed & Average Velocity |
 76%
From NCERT
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Buses ply between two towns, \((A,B)\) separated by \(6~\text{km:}\) those going from \(A\) towards \(B\) go at \(20~\text{km/h}\) while those going from \(B\) to \(A\) go at \(30~\text{km/h}.\) If a passenger were to make a round trip from \(A\) to \(B\) and back, without stopping, his average speed will be:
| 1. | \(25~\text{km/h}\) | 2. | \(24~\text{km/h}\) |
| 3. | \(27~\text{km/h}\) | 4. | \(28~\text{km/h}\) |
Subtopic: Â Average Speed & Average Velocity |
 82%
From NCERT
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Two cars \(A\) & \(B\) move in parallel lanes along the same highway, with constant forward accelerations. Both cars cross the same marker \((X)\) at \(t=0\) (simultaneously) and after some time, they cross a second marker \((Y)\) at \(t=T\) (again, simultaneously). Let the initial velocities of \(A,B\) be \(u_{\Large_A},u_{\Large_B}\) and the final velocities be \(v_{\Large_A},v_{\Large_B}.\)
| Assertion (A): | If \(u_{\Large_A}>u_{\Large_B}\) then \(v_{\Large_B}>v_{\Large_A}\) and vice-versa. |
| Reason (R): | Since they traverse the same distance in the same time \((T),\) their average velocities must be equal: the average velocity being the mean of the initial and final velocities. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Â Average Speed & Average Velocity |
 58%
From NCERT
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Two particles move with constant speeds of \(3~\text{m/s}\) and \(5~\text{m/s}\) along the periphery of a square \(ABCD\) of side \(2~\text{m}\) (as shown). They start from \(A\) at the same time.
Their average velocities, over the period of motion till they meet for the first time, are:
1. \(3~\text{m/s},5~\text{m/s}\)
2. \(\sqrt5~\text{m/s},\sqrt5~\text{m/s}\)
3. \({\Large\frac{\sqrt5}{3}}~\text{m/s},{\Large\frac{\sqrt5}{5}}~\text{m/s}\)
4. \({\Large\frac{\sqrt5}{5}}~\text{m/s},{\Large\frac{\sqrt5}{3}}~\text{m/s}\)
Their average velocities, over the period of motion till they meet for the first time, are:
1. \(3~\text{m/s},5~\text{m/s}\)
2. \(\sqrt5~\text{m/s},\sqrt5~\text{m/s}\)
3. \({\Large\frac{\sqrt5}{3}}~\text{m/s},{\Large\frac{\sqrt5}{5}}~\text{m/s}\)
4. \({\Large\frac{\sqrt5}{5}}~\text{m/s},{\Large\frac{\sqrt5}{3}}~\text{m/s}\)
Subtopic: Â Average Speed & Average Velocity |
 58%
From NCERT
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