A drunkard walking in a narrow lane takes \(5\) steps forward and \(3\) steps backward, followed again by \(5\) steps forward and \(3\) steps backward, and so on. Each step is \(1\) m long and requires \(1\) s. There is a pit on the road \(13\) m away from the starting point. The drunkard will fall into the pit after:
1. \(37\) s
2. \(31\) s
3. \(29\) s
4. \(33\) s
A jet airplane travelling at the speed of \(500~\text{km/h}\) ejects its products of combustion at the speed of \(1500~\text{km/h}\) relative to the jet plane. What is the speed of the latter with respect to an observer on the ground?
1. \(1000~\text{km/h}\)
2. \(500~\text{km/h}\)
3. \(1500~\text{km/h}\)
4. \(2000~\text{km/h}\)
A car moving along a straight highway at a speed of \(126~\text{km/h}\) is brought to a stop within a distance of \(200~\text{m}.\) How long does it take for the car to stop?
1. \(10.2~\text{s}\)
2. \(9.6~\text{s}\)
3. \(11.4~\text{s}\)
4. \(6.7~\text{s}\)
The figure gives the \((x\text-t)\) plot of a particle in a one-dimensional motion. Three different equal intervals of time are shown. The signs of average velocity for each of the intervals \(1,\) \(2\) and \(3,\) respectively are:
1. | \(-,-,+\) | 2. | \(+,-,+\) |
3. | \(-,+,+\) | 4. | \(+,+,-\) |
The figure gives a speed-time graph of a particle in motion along the same direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude?
1. | Interval 2 | 2. | Interval 1 |
3. | Interval 3 | 4. | Equal in all intervals |
A boy standing on a stationary lift (open from above) throws a ball upwards with the maximum initial speed he can, equal to \(49~\text{ms}^{-1}.\) How much time does the ball take to return to his hands?
1. | \(5\) s | 2. | \(10\) s |
3. | \(15\) s | 4. | \(7\) s |
1. | zero velocity. | 2. | zero acceleration. |
3. | non-zero velocity. | 4. | non-zero acceleration. |
If a particle is moving along a straight line with increasing speed, then:
1. | its acceleration is negative. |
2. | its acceleration may be decreasing. |
3. | its acceleration is positive. |
4. | both (2) & (3) |
When the velocity of a body is variable, then:
1. | its speed may be constant |
2. | its acceleration may be constant |
3. | its average acceleration may be constant |
4. | all of the above |
A particle moves with velocity \(v_1\) for time \(t_1\) and \(v_2\) for time \(t_2\) along a straight line. The magnitude of its average acceleration is:
1.
2.
3.
4.