Q. No.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 |
The graph between the displacement \(x\) and time \(t\) for a particle moving in a straight line is shown in the figure.
During the interval OA, AB, BC and CD the acceleration of the particle is:
| OA | AB | BC | CD | |
| 1. | + | 0 | + | + |
| 2. | – | 0 | + | 0 |
| 3. | + | 0 | – | + |
| 4. | – | 0 | – | 0 |
A particle moves along a straight line and its position as a function of time is given by \(x= t^3-3t^2+3t+3\)
| 1. | stops at \(t=1~\text{s}\) and reverses its direction of motion. |
| 2. | stops at \(t= 1~\text{s}\) and continues further without a change of direction. |
| 3. | stops at \(t=2~\text{s}\) and reverses its direction of motion. |
| 4. | stops at \(t=2~\text{s}\) and continues further without a change of direction. |
| 1. | \(24~\text m\) | 2. | \(40~\text m\) |
| 3. | \(56~\text m\) | 4. | \(16~\text m\) |
The displacement time graph of a moving particle is shown in the figure below. The instantaneous velocity of the particle is negative at the point:
| 1. | D | 2. | F |
| 3. | C | 4. | E |
A particle shows distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point:
1. B
2. C
3. D
4. A
A particle moves in a straight line, according to the law \(x=4a[t+a\sin(t/a)], \) where \(x\) is its position in metres, \(t\) is in seconds & \(a\) is some constant, then the velocity is zero at:
| 1. | \(x = 4 a^2\pi\) metres | 2. | \(t = \pi\) sec |
| 3. | \(t =0\) sec | 4. | none of the above |
The displacement \((x)\) of a point moving in a straight line is given by; \(x=8t^2-4t.\) Then the velocity of the particle is zero at:
| 1. | \(0.4~\text s\) | 2. | \(0.25~\text s\) |
| 3. | \(0.5~\text s\) | 4. | \(0.3~\text s\) |
The graph below shows position as a function of time for two trains running on parallel tracks.
Which of the following statements is true?
| 1. | At time \(t_B \) both the trains have the same velocity |
| 2. | Both the trains have the same velocity at some time after \(t_B \) |
| 3. | Both the trains have the same velocity at some time before \(t_B \) |
| 4. | Both the trains have the same acceleration |
Among the four graphs shown in the figure, there is only one graph for which average velocity over the time interval \((0,T)\) can vanish for a suitably chosen \(T\). Select the graph.
| 1. |  |
2. |  |
| 3. |  |
4. |  |
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