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.

Given,

Distance covered in one step = 1 m

Time required for one step = 1 s

Distance for pit from initial position = 13 m

Time taken to move 5m forward = 5 s

Time taken to move 3m backward = 3 s

Speed of the drunkard = 1 m/s (∵from above two observations)

Net distance covered = 5-3 = 2 m

Net time required to cover 2m = 8 s

Total 6 complete forward-backward cycles possible.

Time taken for 6 cycles = 36 s

Distance covered in 6 cycles = 12 m

∴ Total time required to cover 13 m = 36 + 1 =37 s

The graph obtained from above data is,