Question

What is the fastest rate (in \(\mathrm{m} / \mathrm{sec}\) and \(\mathrm{mph}\) ) that pain information can be transmitted?

Short answer

The fastest rate that pain information can be transmitted is approximately 120 meters per second (m/s) and 268.45 miles per hour (mph).

Step-by-step solution

Calculate the speed in meters per second

The speed of nerve impulses is 120 meters per second (m/s). This value is already given.

Convert meters per second to miles per hour

To convert the speed from meters per second (m/s) to miles per hour (mph), we need to use the conversion factors. Given that 1 meter = 0.000621371 mile and 1 second = 1/3600 hour, we can rewrite the speed in miles per hour. \(Speed (mph) = 120\frac{meters}{second} \cdot 0.000621371\frac{miles}{meter} \cdot 3600\frac{seconds}{hour}\)

Calculate the speed in miles per hour

Now, we simply multiply the factors together to determine the speed in miles per hour. \(Speed (mph) = 120 \cdot 0.000621371 \cdot 3600\) \(Speed (mph) \approx 268.45\) The fastest rate that pain information can be transmitted is approximately 120 meters per second (m/s) and 268.45 miles per hour (mph).

Key concepts

Pain Transmission

Pain transmission is how our body sends signals of pain to the brain. This process involves special nerve fibers called nociceptors, which sense harm or potential injury.
Once these nociceptors detect a painful stimulus, they send nerve impulses through the spinal cord to the brain. The brain then interprets these signals as pain.
Let's break it down further:

• Nociceptors Activation: These nerve endings get activated by heat, pressure, or chemicals.
• Signal Pathway: The signal travels via nerve fibers to the spinal cord and then to the brain.
• Response: The brain processes these signals to help us react quickly to avoid harm.

Understanding this process is vital as it highlights how quickly our bodies work to protect us by warning of danger.

Nerve Impulses

Nerve impulses are electrical signals that travel through neurons to communicate information. These signals move quickly for efficient body responses.
Here's how they work:

• Generation: An impulse starts when a neuron receives a strong enough stimulus.
• Propagation: The impulse travels along the axon of the neuron.
• Speed: In myelinated neurons, impulses can travel at speeds up to 120 meters per second (m/s).

This speed allows for quick reflexes and rapid transmission of messages across the body. Efficient nerve impulse speed is crucial for survival as it enables fast responses to the environment.

Conversion of Units

Converting units is essential in applying mathematical concepts to real-world scenarios. In the context of nerve impulse speed, converting meters per second (m/s) to miles per hour (mph) gives a more relatable understanding.
Here's how it's done:

• Identify Conversion Factors:
  • 1 meter = 0.000621371 miles
  • 1 second = 1/3600 hours
• Set Up the Equation: Use these factors to convert speed from (m/s) to (mph).
• Calculate: Multiply 120 m/s by the conversion factors to get approximately 268.45 mph.

Converting units helps in comparing speeds in different systems, making it easier to comprehend physical phenomena in everyday terms.