/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 2 You step onto a hot beach with y... [FREE SOLUTION] | 91Ó°ÊÓ

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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
The impulse takes approximately 0.0164 seconds to reach the brain.

Step by step solution

01

Identify the Given Information

We know the average speed of the nerve impulse is \(110 \, \text{m/s}\) and the distance the impulse travels is \(1.8 \, \text{m}\).
02

Understand the Formula for Time

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

Plug Values into the Formula

Substitute \(d = 1.8 \, \text{m}\) and \(v = 110 \, \text{m/s}\) into the formula: \( t = \frac{1.8}{110} \).
04

Calculate the Time

Perform the division: \( t = \frac{1.8}{110} \approx 0.01636 \, \text{seconds}\).

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Key Concepts

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

Nerve Impulse Speed
Nerve impulse speed is a fascinating aspect of our biological wiring. It is the rate at which the signals are transmitted along the nerves, enabling us to react swiftly to different stimuli. In our exercise, the nerve impulses travel from the foot to the brain, allowing the brain to perceive heat and respond appropriately.
Our body's transmission lines, known as neurons, have specialized properties that aid this high-speed communication. The average speed in the exercise is given as 110 meters per second, which reflects the typical speed of nerve signals in some types of neurons, although speeds can vary widely.
If a danger is detected, the nerve impulses quickly alert the central nervous system. This rapid transmission is vital to help prevent injuries by triggering reflex actions or responses.
Understanding nerve impulse speeds helps elucidate the incredible efficiency of our nervous system and its role in keeping us safe and responsive.
Distance-Time Calculation
In physics, calculating how long it takes for something to travel a certain distance is a fundamental task. This exercise asks us to find out how long a nerve impulse takes to travel from your foot to your brain if the foot is burnt. The distance covered by the nerve impulse is 1.8 meters.
Using the formula for time, we can determine how long this nerve impulse journey takes. This formula includes distance (d) and speed (v), and it tells us how to figure out the time (t):
  • Formula: \( t = \frac{d}{v} \)
Understanding this calculation helps us convert raw measurements into meaningful information, like understanding reaction times and signal speeds in the nervous system.
It's a practical tool for deciphering many real-world physics problems, from determining travel times to analyzing how fast signals move in a race.
Average Speed Formula
The average speed formula reveals how fast something is moving, on average, over a specific distance. It is especially useful when you need to determine an overall speed with constants over time, such as nerve impulse speed in our scenario.
The formula looks like this:
  • Average speed (\( v \)): \( v = \frac{d}{t} \)
In this exercise, we worked backward using a variation of this formula to determine the time taken, given the speed and distance. By solving \( t = \frac{d}{v} \), we get the specific time the impulse takes to travel a known distance at a known average speed.
When applying this concept, it is crucial to keep all units consistent, usually using meters for distance and seconds for time (as seen here). This helps ensure accurate calculations essential for scientific research and practical safety measures.

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Most popular questions from this chapter

A jogger accelerates from rest to \(3.0 \mathrm{~m} / \mathrm{s}\) in \(2.0 \mathrm{~s}\). A car accelerates from 38.0 to \(41.0 \mathrm{~m} / \mathrm{s}\) also in \(2.0 \mathrm{~s}\). (a) Find the acceleration (magnitude only) of the jogger. (b) Determine the acceleration (magnitude only) of the car. (c) Does the car travel farther than the jogger during the \(2.0 \mathrm{~s}\) ? If so, how much farther?

A ball is dropped from rest from the top of a cliff that is \(24 \mathrm{~m}\) high. From ground level, a second ball is thrown straight upward at the same instant that the first ball is dropped. The initial speed of the second ball is exactly the same as that with which the first ball eventually hits the ground. In the absence of air resistance, the motions of the balls are just the reverse of each other. Determine how far below the top of the cliff the balls cross paths.

Two runners start one hundred meters apart and run toward each other. Each runs ten meters during the first second. During each second thereafter, each runner runs ninety percent of the distance he ran in the previous second. Thus, the velocity of each person changes from second to second. However, during any one second, the velocity remains constant. Make a position-time graph for one of the runners. From this graph, determine (a) how much time passes before the runners collide and (b) the speed with which each is running at the moment of collision.

Interactive Solution \(\underline{2.31}\) at offers help in modeling this problem. A car is traveling at a constant speed of \(33 \mathrm{~m} / \mathrm{s}\) on a highway. At the instant this car passes an entrance ramp, a second car enters the highway from the ramp. The second car starts from rest and has a constant acceleration. What acceleration must it maintain, so that the two cars meet for the first time at the next exit, which is \(2.5 \mathrm{~km}\) away?

The three-toed sloth is the slowest moving land mammal. On the ground, the sloth moves at an average speed of \(0.037 \mathrm{~m} / \mathrm{s}\), considerably slower than the giant tortoise, which walks at \(0.076 \mathrm{~m} / \mathrm{s}\). After 12 minutes of walking, how much further would the tortoise have gone relative to the sloth?

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