Question

Alex goes cruising on his dirt bike. He rides 700m north, 300m east, 400m north, 600m west, 1200m south, 300m east and finally 100m north. What distance did he cover? What was his displacement?

Answer 1

Alex's displacement is zero. The distance traveled is 3600 m.

Refer to the attached diagram.

Displacement is the shortest distance between the starting and the ending point.

Take the starting point as the origin and determine his position as he moves on his bike.

Alex moves 700 m North along the path AB, 300 m east along BC, 400 m north along CD. At point D, Alex has coordinates : 1100 m north and 300 m east. He then moves 600 m west along DE. At point E, his coordinates are: 1100 m North and 300 m west. He then moves 1200 m south along EF. At point F, his coordinates are 100 m south and 300 m west. He then moves 300 m towards East, along FG, when he is 100 m south of his starting point. He then moves 100 m  North and then arrives at his starting point.

Since Alex arrives at his starting point at the end of his motion, the distance between the starting and the ending point of his journey is zero. Hence his displacement is zero.

Distance is a scalar. Hence the total distance is equal to the total path length traveled by Alex. This can be calculated by adding the individual distances, what ever be the direction in which he would have traveled.

$distance=700 m+300 m+400 m+600 m+ 1200 m+ 300 m+100 m=3600 m$

The total distance Alex travels is equal to 3600 m