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

Distance space covered space in space 1 space step space equals space 1 space straight m space Time space taken space equals space 1 space sec space Time space taken space to space move space first space 5 space straight m space forward space equals space 5 space straight s space Time space taken space to space move space 3 space straight m space backwards space equals space 3 space sec Net space distance space covered space equals space 5 space minus space 3 space equals space 2 space straight m space Net space time space taken space to space cover space 2 space straight m space equals space 8 space sec Therefore comma space Drunkard space covers space 2 space straight m space in space 8 space straight s comma space 4 straight m space in space 16 space sec comma space 6 space straight m space in space 24 space sec space and space 8 space straight m space in space 32 space sec. space That space is comma space the space drunkard space will space cover space straight a space distance space of space 5 straight m space in space space the space next space 5 space sec. space straight A space total space distance space of space 13 space straight m space is space covered space and space he space falls space into space the space pit. space Therefore comma Net space time space taken space by space the space drunkard space to space cover space 13 space straight m space equals space 32 plus 5 space equals space 37 space sec

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