A gram-negative bacterium moves along a flat surface. What is the maximum displacement of the bacterium during a 1-hour period if the bacterium moves at a constant speed of 25 µm/s?

Question

A gram-negative bacterium moves along a flat surface.  What is the maximum displacement of the bacterium during a 1-hour period if the bacterium moves at a constant speed of 25 µm/s?

Quizplus · Accepted Answer

11ecba2d_1317_4761_a3bf_339ac27106fb_MD0008_00 Velocity (v) is a variable of translational motion that expresses the displacement (Δx or x_f− x_i) of a moving object per unit time (t). Unlike speed, which is the magnitude of velocity, velocity is a vector quantity characterized by both magnitude and direction. Consequently, the speed of an object relates to distance, but the velocity of an object relates to displacement. Due to the relationship between velocity and displacement, the x- and y-components of displacement (Δx and Δy) for an object moving through an x,y-coordinate system can be evaluated by multiplying the x- and y-component velocities (v_x and v_y, respectively) by the interval of time for that motion: 11ecba2d_1317_6e72_a3bf_b3043cc2b595_MD0008_00 11ecba2d_1317_6e73_a3bf_4de5e6fe7067_MD0008_00 In this question, a gram-negative bacterium moves along a flat surface at a constant speed of 25 µm/s for 1 hour. Although the bacterium likely moves across the surface along a winding path, the maximum possible displacement from the origin would occur if the movement of the bacteria traces a straight path. In such a case, the constant speed of 25 µm/s would translate to a constant velocity of 25 µm/s because the bacterium moves in only one direction. After selecting an x,y-coordinate system oriented such that the motion of the bacterium takes place along only the x-axis (no y-axis displacement, v_y = 0), the maximum possible displacement of the bacterium over a span of 1 hour can be determined by substituting velocity and time into the equation for displacement: 11ecba2d_1317_6e74_a3bf_6bbe97b8d916_MD0008_00 Converting all values to standard units results in: 11ecba2d_1317_6e75_a3bf_cd6e63449031_MD0008_00 11ecba2d_1317_6e76_a3bf_f969e93037b2_MD0008_00 11ecba2d_1317_6e77_a3bf_c9e111fda42c_MD0008_00 Therefore, the maximum hourly displacement of a bacterium moving along a flat surface at a constant speed of 25 µm/s is 9 × 10⁻² m (Choice D). Educational objective: The displacement of an object is calculated as the average velocity of the object multiplied by the interval of time during which the object moves. The speed of an object is equal to the magnitude of the velocity of the object.

A Gram-Negative Bacterium Moves Along a Flat Surface