Axonal Vesicle Travel Time Calculation

This solution calculates the time required for a vesicle to travel the length of an axon based on its distance and average velocity.

Problem Setup

The question involves an axonal process with the following characteristics:

• Distance: The axon length is $D = 2$ meters.
• Velocity: The average speed of a vesicle is $v = 1\text{ }\mu\text{m}/\text{s}$.
• Goal: Calculate the time ($t$) for the vesicle to travel from the cell body to the axonal tip.

Unit Consistency Check

To perform the calculation, the units must be consistent. The distance is given in meters (m), and the velocity is in micrometers per second ($\mu\text{m}/\text{s}$). We must convert meters to micrometers. Recall that $1$ meter is equal to $10^6$ micrometers.

Convert the distance to micrometers: $D = 2 \text{ m} \times \frac{10^6 \text{ }\mu\text{m}}{1 \text{ m}} = 2 \times 10^6 \text{ }\mu\text{m}$

Time Calculation

The relationship between time, distance, and velocity is given by the formula: $t = \frac{D}{v}$

Substitute the distance (in $\mu$m) and the velocity (in $\mu$m/s) into the formula:

$t = \frac{2 \times 10^6 \text{ }\mu\text{m}}{1 \text{ }\mu\text{m}/\text{s}}$

Performing the division yields:

$t = 2 \times 10^6 \text{ seconds}$

Final Answer Derivation

The calculated time is $2 \times 10^6$ seconds. This matches one of the provided options.