Q. No.The displacement \(x\) of a particle moving in one dimension under the action of a constant force is related to time \(t\) by the equation \(t=\sqrt{x}+3,\) where \(x\) is in meters and \(t\) is in seconds. What is the displacement of the particle from \(t=0~\text s\) to \(t = 6~\text s?\)
1. \(0\)
2. \(12~\text m\)
3. \(6~\text m\)
4. \(18~\text m\)
A car moves with a speed of \(60\) km/h for \(1\) hour in the east direction and with the same speed for \(30\) min in the south direction. The displacement of the car from the initial position is:
| 1. | \(60\) km | 2. | \(30 \sqrt{2}\) km |
| 3. | \(30 \sqrt{5}\) km | 4. | \(60 \sqrt{2}\) km |
| Assertion (A): | Displacement of a body may be zero when distance travelled by it is not zero. |
| Reason (R): | The displacement is the longest distance between initial and final position. |
| 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. | Both (A) and (R) are False. |
Given below are two statements:
| Assertion (A): | Position-time graph of a stationary object is a straight line parallel to the time axis. |
| Reason (R): | For a stationary object, the position does not change with 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. | Both (A) and (R) are False. |
The coordinate of an object is given as a function of time by \(x = 7 t - 3 t^{2}\), where \(x\) is in metres and \(t\) is in seconds. Its average velocity over the interval \(t=0\) to \(t=4\) is will be:
1. \(5\) m/s
2. \(-5\) m/s
3. \(11\) m/s
4. \(-11\) m/s
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 moves with a velocity \(v = αt^{3}\) along a straight line. The average speed in time interval \(t=0\) to \(t=T\) will be:
1. \(\alpha T^3\)
2. \(\frac{αT^{3}}{2}\)
3. \(\frac{\alpha T^3}{3}\)
4. \(\frac{αT^{3}}{4}\)
If a body travels some distance in a given time interval, then for that time interval, its:
| 1. | Average speed ≥ |Average velocity| |
| 2. | |Average velocity| ≥ Average speed |
| 3. | Average speed < |Average velocity| |
| 4. | |Average velocity| must be equal to average speed. |
1. \(\frac{3v}{4}\)
2. \(\frac{v}{3}\)
3. \(\frac{2v}{3}\)
4. \(\frac{4v}{3}\)
The relation \(3t = \sqrt{3x} + 6\) describes the displacement of a particle in one direction where \(x\) is in metres and \(t\) in seconds. The displacement, when velocity is zero, is:
| 1. | \(24\) metres | 2. | \(12\) metres |
| 3. | \(5\) metres | 4. | zero |
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