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In summary, the conversation discusses the use of equations to determine the final velocity of a freight train that accelerates at a rate of 0.0400 m/s^2 for 8.00 min, starting with an initial velocity of 4.00 m/s. The first equation, v=v0 + at, is the correct equation to use and gives a final velocity of 23.2 m/s. The use of the second and third equations is considered roundabout and may result in incorrect calculations.

- #1

remcalister

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## Homework Statement

Freight trains can produce only relatively small acceleration and decelerations.

(a) What is the final velocity of a freight train that accelerates at a rate of 0.0400 m/s^2 for 8.00 min, starting with an initial velocity of 4.00 m/s?

## Homework Equations

v=v0 + at

x=x0 +v0t +1/2at^2

v^2=v0^2 +2a(x-x0)

## The Attempt at a Solution

Why can't i use the first equation I listed to solve this problem? Using that equation, you end up with v = 76.8 m/s

If you first use the second equation, and then the third equation, you end up with v = 23.2 m/s

Thanks in advance!

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- #2

billy_joule

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The first eqn gives the same as the 2nd and third.

v = 76.8 m/s is wrong, 23.2 m/s is right you may have pressed a wrong button on your calculator.

v=v0 + at

v = 4 m/s + (0.04 m/s^2)*(8 min * 60s/min) = 23.2 m/s

- #3

olivermsun

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The first equation is exactly what you're supposed to use. Using the second and third seems roundabout.

But how are you getting 76.8 m/s with the first equation? Can you show your work?

- #4

remcalister

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Oh goodness, it's been a long weekend haha. I accidentally set it up as 4 m/s TIMES (0.04m/s^2)(480s).

Thanks guys

- #5

HalfLostAndSearching

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As a scientist, it is important to understand the limitations of equations and when they can be applied. In this case, the equation v=v0 + at assumes that the acceleration is constant throughout the entire time period. However, in the problem given, it is stated that freight trains can only produce relatively small acceleration and decelerations. This means that the acceleration may not be constant and could change over time. Therefore, the equation v=v0 + at may not accurately represent the situation and it is necessary to use the more general equations x=x0 +v0t +1/2at^2 and v^2=v0^2 +2a(x-x0) to account for any changes in acceleration. These equations take into account the initial velocity, final velocity, and displacement, making them more appropriate for this problem. It is important to always carefully consider the given information and choose the appropriate equation to use in order to accurately solve a problem.

## FAQ: Not sure why I can't use v=v0 + at on this problem.

## What does the equation v=v0 + at represent?

The equation v=v0 + at represents the relationship between an object's initial velocity, its acceleration, and its final velocity after a certain amount of time has passed. It is known as the kinematic equation for constant acceleration.

## Why can't I use the equation v=v0 + at for this problem?

There are several reasons why this equation may not be applicable to a certain problem. It is important to check the given information and ensure that the object has constant acceleration, the initial velocity is known, and the time interval is specified. Additionally, this equation does not account for other factors such as air resistance or changing forces.

## What are some alternative equations that I can use?

Depending on the given information and the type of problem, there are several other kinematic equations that can be used instead of v=v0 + at. These include equations for displacement, final velocity, and time. It is important to choose the appropriate equation based on the given information and the unknown variable.

## Can I use the equation v=v0 + at for objects with changing acceleration?

No, the equation v=v0 + at is only applicable for objects with constant acceleration. If the acceleration is changing, a different equation, such as the equation for average acceleration, should be used.

## How can I check if I have correctly applied the equation v=v0 + at?

To ensure that the equation v=v0 + at has been correctly applied, you can check if the units of the equation match. The units for velocity are meters per second (m/s), the units for initial velocity are also meters per second (m/s), and the units for acceleration are meters per second squared (m/s^2). If the units do not match, then the equation has been incorrectly applied.

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