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 |
The position-time \((x\text-t)\) graphs for two children \(A\) and \(B\) returning from their school \(O\) to their homes \(P\) and \(Q\) respectively are shown in the graph. Choose the incorrect statement.
1. | \(B\) reaches home faster than \(A.\) |
2. | \(B\) overtakes \(A\) on the road twice. |
3. | \(B\) walks faster than \(A.\) |
4. | \(A\) lives closer to the school than \(B.\) |
A car moving along a straight highway with a speed of \(126\) km/h is brought to a stop within a distance of \(200\) m. How long does it take for the car to stop?
1. | \(10.2\) s | 2. | \(9.6\) s |
3. | \(11.4\) s | 4. | \(6.7\) 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 \(1,\) \(2\) & \(3,\) 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 |
A passenger arriving in a new town wishes to go from the station to a hotel located \(10\) km away on a straight road from the station. A dishonest cabman takes him along a circuitous path \(23\) km long and reaches the hotel in \(28\) min. The average speed of the taxi is:
1. | \(30\) km/h | 2. | \(49.3\) km/h |
3. | \(55.6\) km/h | 4. | \(60\) km/h |
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 |
A body in one-dimensional motion has zero speed at an instant. At that instant, it must have:
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) |