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 $500 km h^{-1}$ ejects its products of combustion at the speed of $1500 km h^{-1}$ relative to the jet plane. What is the speed of the latter with respect to an observer on the ground?

$1. 1000 km h^{-1}$
$2. 500 km h^{-1}$
$3. 1500 km h^{-1}$
$4. 2000 km h^{-1}$

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 \((\mathrm{x-t})\) 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:

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?

A boy standing on a stationary lift (open from above) throws a ball upwards with the maximum initial speed he can, equal to $49$ $m$ $s^{-1}.$  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 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:

If a particle is moving along a straight line with increasing speed, then:

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