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Chapter 2: Problem 4

You step onto a hot beach with your bare feet. A nerve impulse, generated in your foot, travels through your nervous system at an average speed of \(110 \mathrm{m} / \mathrm{s} .\) How much time does it take for the impulse, which travels a distance of \(1.8 \mathrm{m},\) to reach your brain?

Short Answer

Expert verified
Approximately 16.36 milliseconds.

Step by step solution

01

Identify the given values

The problem provides that the nerve impulse travels at a speed of \(110 \text{ m/s}\), and the distance from your foot to your brain is \(1.8 \text{ m}\).
02

Recall the formula for time

The formula to calculate time when speed and distance are known is: \[ t = \frac{d}{v} \]where \(t\) is time, \(d\) is distance, and \(v\) is speed.
03

Substitute the known values

Substitute the given distance (\(1.8 \text{ m}\)) and speed (\(110 \text{ m/s}\)) into the formula: \[ t = \frac{1.8}{110} \]
04

Calculate the time

Perform the division:\[ t = \frac{1.8}{110} = 0.01636 \]
05

Convert to milliseconds

To convert seconds to milliseconds, multiply by 1000. Therefore:\[ t = 0.01636 \times 1000 = 16.36 \text{ milliseconds} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Velocity and Speed
In physics, understanding the concepts of velocity and speed is fundamental. Speed is a scalar quantity, which means it only has magnitude (how fast an object is moving). On the other hand, velocity is a vector quantity. This means it includes both magnitude and direction. For example, if you say something is moving at 60 km/h, you're referring to speed. If you say it's moving at 60 km/h north, you're referring to velocity.
  • Using the formula for speed: speed = distance / time, helps you determine how quickly an object is moving regardless of its direction.
  • Velocity adds an additional layer by requiring both speed and direction.
  • In our nerve impulse scenario, we use the speed of 110 m/s, ignoring the direction to focus on how fast it reaches the brain.
Keep in mind that while calculating such quick events like nerve impulses, speed and velocity can be interchanged if direction isn't considered.
Distance and Time Calculation
Calculating the time it takes for a moving object or event to travel a certain distance is a common necessity in physics. The formula for this is derived from rearranging the basic speed formula: time = distance / speed. This means you can easily find out how long something takes if you know how far it needs to go and its rate of travel.
  • Identify the distance and the speed. In our example, the nerve impulse travels 1.8 meters and its speed is 110 m/s.
  • Plug these values into the equation: time = distance / speed, yielding 1.8 m / 110 m/s.
  • Performing the division gives the time in seconds, crucial in quickly occurring events like nerve impulses.
One thing to note is the importance of units. Always make sure your units are consistent (e.g., meters for distance and meters per second for speed), ensuring accurate time calculation in seconds.
Neuroscience Concepts
The way our bodies transmit information is truly fascinating and ties deeply into neuroscience. When your foot steps on a hot surface, a nerve impulse is generated as an electrical signal. Your body uses these nerve impulses to communicate between the brain and different parts of the body.
  • Nerve impulses travel through the nervous system at rapid speeds, measured in meters per second.
  • This speed can vary depending on the type of nerve involved. For motor nerves, the speed can go up to 120 m/s.
  • Understanding this speedy transmission helps us appreciate reflexive responses, like pulling your foot away from something hot, which happens in mere milliseconds.
It's amazing to consider that such crucial processes happen in fractions of a second, highlighting the efficiency and complexity of our nervous system.

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Most popular questions from this chapter

Electrons move through a certain electric circuit at an average speed of \(1.1 \times 10^{-2} \mathrm{m} / \mathrm{s} .\) How long (in minutes) does it take an electron to traverse \(1.5 \mathrm{m}\) of wire in the filament of a light bulb?

The leader of a bicycle race is traveling with a constant velocity of \(+11.10 \mathrm{m} / \mathrm{s}\) and is \(10.0 \mathrm{m}\) ahead of the second-place cyclist. The secondplace cyclist has a velocity of \(+9.50 \mathrm{m} / \mathrm{s}\) and an acceleration of \(+1.20 \mathrm{m} / \mathrm{s}^{2}\). How much time elapses before he catches the leader?

A car is traveling along a straight road at a velocity of \(+36.0 \mathrm{m} / \mathrm{s}\) when its engine cuts out. For the next twelve seconds the car slows down, and its average acceleration is \(\bar{a}_{1} .\) For the next six seconds the car slows down further, and its average acceleration is \(\bar{a}_{2} .\) The velocity of the car at the end of the eighteen-second period is \(+28.0 \mathrm{m} / \mathrm{s}\). The ratio of the average acceleration values is \(\bar{a}_{1} / \bar{a}_{2}=1.50 .\) Find the velocity of the car at the end of the initial twelve-second interval.

An Australian emu is running due north in a straight line at a speed of \(13.0 \mathrm{m} / \mathrm{s}\) and slows down to a speed of \(10.6 \mathrm{m} / \mathrm{s}\) in \(4.0 \mathrm{s}\). (a) What is the direction of the bird's acceleration? (b) Assuming that the acceleration remains the same, what is the bird's velocity after an additional \(2.0 \mathrm{s}\) has elapsed?

In getting ready to slam-dunk the ball, a basketball player starts from rest and sprints to a speed of \(6.0 \mathrm{m} / \mathrm{s}\) in \(1.5 \mathrm{s} .\) Assuming that the player accelerates uniformly, determine the distance he runs.
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