Question
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. Plot the x-t graph of his motion. Determine graphically and otherwise how long the drunkard takes to fall in a pit 13 m away from the start.
Solution
Length of 1 step taken by drunkard = 1 m
Time to take 1 step = 1 sec
So, the speed of the drunkard = 1 m/s
When he walk 5 steps forward, its position is 5m at time 5s.
After walking 3 steps backward, the position of drunkard at 8 sec becomes 2m.
So, the position- time graph is as shown in figure.
Time to take 1 step = 1 sec
So, the speed of the drunkard = 1 m/s
When he walk 5 steps forward, its position is 5m at time 5s.
After walking 3 steps backward, the position of drunkard at 8 sec becomes 2m.
| Time, t (sec) | Distance, x (m) |
| 5 | 5 |
| 8 | 2 |
| 13 | 7 |
| 16 | 9 |
| 24 | 6 |
So, the position- time graph is as shown in figure.
