2, a-f please show work

Mammalian cell 2. Listeria, like all bacteria, emit small molecules as waste products or for signaling. Here we will consider a "race" between a Listeria bacterium (about 1 um across) and a chemical signal it emits while inside a much larger (15 pm) mammalian cell. Suppose the Listeria bacterium, when at one end of the mammalian cell, emits a pulse of signaling molecules which begin diffusing through the mammalian cell. The Listeria then moves along a straight line from one end of the mammalian cell to the other, a. Write down the equation for the rms distance, assuming the diffusion is three-dimensional. Explain in words what the rms distance means (that is, what it tells us about a diffusion process). L/steria b. Using a diffusion constant of 200 um/s, about how long does it take the signaling molecules to reach the other side of the mammalian cell? c. If the bacterium moves at a constant speed of 5 m/s, how long does it take the Listeria to reach the other side of the mammalian cell? d. On the graph below, plot two lines: one representing the position of the Listeria as a function of time, and the other representing the rms distance of the signaling molecules as a function of time. (Use the numbers provided above and the scale on the time axis to calculate the position and firms, and use an appropriate scale for the vertical axis.) Position/rems (mm) t(s) 0 10 20 30 40 50 60 e. Which motion is faster in this scenario: the directed, coherent motion of the bacterium or the random diffusion of the chemical? How can you tell? Is there any scenario when they would be reversed? 1. About how big would a cell have to be for the directed, coherent motion of the bacterium to be faster than the random diffusion of the chemical