The bacterium Escherichia coli (or E. coli) is a...

The bacterium Escherichia coli (or $E$. coli) is a singlecelled organism that lives in the gut of healthy humans and animals. When grown in a uniform medium rich in salts and amino acids, it swims along zig-zag paths at a constant speed changing direction at varying time intervals. Figure FIGURE P1.61 P1.61 shows the positions of an $E$. coli as it moves from point A to point J. Each segment of the motion can be identified by two letters, such as segment BC. During which segments, if any, does the bacterium have the same a. Displacement? b. Speed? c. Velocity?

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Key Concepts

Displacement

Displacement is a vector quantity defined as the change in position from the starting point to the ending point. It depends only on these two positions, not on the path taken, and therefore emphasizes both magnitude and direction, making it possible for different segments to have the same displacement if their start and end points coincide.

Speed

Speed is a scalar quantity that measures the total distance traveled per unit time, without any consideration for direction. It captures how fast an object is moving along its path, and since it is independent of the direction of travel, different segments of a motion can have the same speed even if the directions differ.

Velocity

Velocity is a vector quantity that describes the rate of change of displacement with respect to time. It provides information about both the magnitude (how fast an object is moving) and the direction of motion, meaning that only segments with both identical displacement and time interval (and thus the same directional change) have the same velocity.

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