A team of microbiologists studies the motion of a single bacterium moving back and forth along a straight glass capillary tube. They establish a one-dimensional coordinate system along the length of the tube such that motion toward the microscope’s light source (to the left as seen by the observer) is defined as the positive direction. At a particular instant the bacterium’s velocity is recorded as +5μms−1.
(1) Identify the physical (left/right) direction in which the bacterium is moving at that instant, and explain how you arrived at your conclusion using the given sign convention.
(2) Another researcher analyzing the same video chooses the opposite orientation, defining motion toward the microscope’s light source as the negative direction. What numerical sign would this second researcher record for the bacterium’s velocity at the same instant? Justify your answer.
(3) Describe qualitatively how changing the sign convention would affect (i) the recorded displacement of the bacterium between any two instants and (ii) the measured distance traveled. Explain your reasoning.
(4) Explain why the choice of sign convention does not alter any physically measurable aspects of the bacterium’s motion, even though the recorded signs of vector quantities change.