Question

Type A nerve fibers in humans can conduct nerve impulses at speeds up to \(140 \mathrm{~m} / \mathrm{s}\) (see Figure 1.17). (a) How fast are the nerve impulses moving in kilometers per hour? (b) How far (in meters) can the impulses travel in \(5.0 \mathrm{~ms}\) ?

Short answer

(a) 504 km/h (b) 0.7 meters

Step-by-step solution

Understanding the Speed Conversion

We need to convert the speed from meters per second (m/s) to kilometers per hour (km/h). First, recall the conversion factors: 1 km = 1000 m and 1 hour = 3600 seconds.

Calculating Speed in km/h

To convert 140 m/s to km/h, multiply by the conversion factor: \[140 \frac{\text{m}}{\text{s}} \times \frac{1 \text{ km}}{1000 \text{ m}} \times \frac{3600 \text{ s}}{1 \text{ hour}} = 504 \frac{\text{km}}{\text{hour}}\]

Understanding the Distance Calculation

We need to find out how far the nerve impulse travels in a given time, 5.0 ms. First, convert milliseconds to seconds: 5.0 ms = 0.005 seconds.

Calculating Distance in Meters

Using the speed of 140 m/s, multiply by the time in seconds to get the distance: \[140 \frac{\text{m}}{\text{s}} \times 0.005 \text{ s} = 0.7 \text{ m}\]

Key concepts

Speed Conversion

When converting speed from one unit to another, it is crucial to use the correct conversion factors. In this exercise, our goal is to change the speed of nerve impulses from meters per second (m/s) to kilometers per hour (km/h). This requires knowledge of the following conversion facts:

• 1 kilometer is equivalent to 1000 meters,
• 1 hour is equivalent to 3600 seconds.

Using these, we can convert the speed of 140 m/s into km/h by the equation: \[140 \frac{\text{m}}{\text{s}} \times \frac{1 \text{ km}}{1000 \text{ m}} \times \frac{3600 \text{ s}}{1 \text{ hour}} = 504 \frac{\text{km}}{\text{hour}}\]
This procedure involves multiplying by the fraction that converts meters to kilometers and seconds to hours, giving us the speed in km/h.

Nerve Impulse Conduction

Nerve impulse conduction is a fascinating process by which signals are transmitted along a nerve fiber. For humans, Type A nerve fibers are known to conduct these impulses very rapidly, up to speeds of 140 m/s. This high speed allows the body to react and adapt quickly to stimuli.

• Nerve fibers use electrical signals to communicate.
• The speed of conduction is influenced by the diameter of the nerve fiber.
• Myelination, or the presence of a myelin sheath, accelerates impulse conduction.

Understanding the conduction speed can help in analyzing how far and how fast impulses can travel within a specific time frame. It's crucial for understanding response times in reflex actions.

Kinematics

Kinematics is the branch of physics that deals with motion, describing how objects move through space and time. In the context of this nerve impulse exercise, kinematics allows us to calculate how far nerve impulses travel over a certain period.
To find the distance an impulse travels, we use the formula:
Distance = Speed × Time.
With a nerve conduction speed of 140 m/s, and considering a duration of 5.0 milliseconds (0.005 seconds), the distance is:\[140 \frac{\text{m}}{\text{s}} \times 0.005 \text{ s} = 0.7 \text{ m}\]
This shows that in just 5 milliseconds, the impulse travels 0.7 meters down the nerve fiber.

Unit Conversion

Unit conversion is an essential skill in physics, allowing us to express measurements in different systems or scales. In this exercise, we converted time and speed from one unit to another.
Converting from milliseconds to seconds involves simple multiplication:

• 1 millisecond equals 0.001 seconds.
• Thus, 5 milliseconds equal 0.005 seconds (5 × 0.001).

Similarly, understanding the conversion of meters per second to kilometers per hour involves multiple conversion steps. Leveraging these skills ensures that all calculations are accurate and appropriately contextualized. Mastery of unit conversions aids students in tackling diverse problems across physics and other sciences.