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

Explanation

Effective distance covered by the drunked in 8 steps in 8s
`=5-3=2m`
The distance travelled by the drunked in 8s=2 metre.
The distance travelled by the drunkard in 32s is 8m.
Now after 32s, if the drunkard will move next 5 steps forward, then he will fall into the pit which is at a distance of 13m from the start.
Therefore, total time taken by drunkard to fall in the pit
`=32+5=37s`
The (x-t) plot is shown in figure.