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• PhysTeacher88
In summary: That is why the solution of the question is a positive value. So, summarizing the conversation, the textbook uses the "big 5" equations for uniform acceleration, but in one equation (vf^2=vi^2 + 2ad) they do not use vectors. This is because when squaring velocity, the direction information is lost. However, not using vectors can lead to incorrect answers for certain questions, such as determining the height of a ball thrown upward. This is because acceleration and displacement also have a direction. The solution is to use vectors for a and d. This could be an oversight on the part of the textbook, as they may have taken the formula from conservation of energy rather than considering it from a kinematics
PhysTeacher88
The textbook (Nelson 11) at my school lists the "big 5" equations for uniform acceleration. In all but one, they use vectors.

For vf^2=vi^2 + 2ad, the opt not to use vectors.

Is there a deep reason why we would not want to use the vectors?

I understand that when you square the velocity, the direction information is lost, however, without making the acceleration and the displacement vectors (textbook reads distance because it's not a vector), students will not get questions like this correct:

A ball is thrown up at 10m/s, how high will it go?

If I treat everything as scalar, we get:

(0m/s) = (10m/s)^2 + (9.8)d

the distance ends up being a negative value, which is clearly not true given the context.

If they at least made the "a" and delta "d" vectors, they would not run into this problem.

I'm guess they took this formula from conservation of energy, rather than thinking about this from a kinematics perspective.

Am I missing something, or is this an oversight?

Cheers,

K

PhysTeacher88 said:
The textbook (Nelson 11) at my school lists the "big 5" equations for uniform acceleration. In all but one, they use vectors.

For vf^2=vi^2 + 2ad, the opt not to use vectors.

Is there a deep reason why we would not want to use the vectors?

I understand that when you square the velocity, the direction information is lost, however, without making the acceleration and the displacement vectors (textbook reads distance because it's not a vector), students will not get questions like this correct:

A ball is thrown up at 10m/s, how high will it go?

If I treat everything as scalar, we get:

(0m/s) = (10m/s)^2 + (9.8)d

the distance ends up being a negative value, which is clearly not true given the context.

If they at least made the "a" and delta "d" vectors, they would not run into this problem.

I'm guess they took this formula from conservation of energy, rather than thinking about this from a kinematics perspective.

Am I missing something, or is this an oversight?

Cheers,

K
What you're missing is that you have the initial velocity, ##v_i##, being positive, which means that ##a## must be negative. So here ##a = -9.8 m/sec^2##.

Also, the probable reason for not using vectors is that they are dealing with motion in one dimension.

It’s a special case of the work-energy theorem which is a scalar equation.
ΔKE= net Work (=F⋅d for constant F)

Last edited:
Mark44 said:
What you're missing is that you have the initial velocity, ##v_i##, being positive, which means that ##a## must be negative. So here ##a = -9.8 m/sec^2##.

Correct.

Also, notice that d also have a sign. It is positive if the motion was upward, and negative if the motion was downward.

## 1. What is the "Misleading Textbook Equation" for vf^2=vi^2 + 2ad?

The "Misleading Textbook Equation" for vf^2=vi^2 + 2ad refers to the commonly used equation for calculating final velocity in a linear motion system. This equation assumes that the initial velocity (vi) is equal to zero, which is not always the case.

## 2. Why is this equation considered misleading?

This equation is considered misleading because it only applies to a specific scenario where the initial velocity is zero. In reality, the initial velocity can have any value, making this equation inaccurate in most cases.

## 3. What are the consequences of using this equation?

Using this equation can lead to incorrect results and a misunderstanding of the underlying physics principles. It can also hinder the ability to accurately predict and analyze the motion of an object.

## 4. Is there a more accurate equation for calculating final velocity?

Yes, there is a more accurate equation for calculating final velocity in a linear motion system. It is vf = vi + at, where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time.

## 5. How can we avoid using the misleading textbook equation?

To avoid using the misleading textbook equation, it is important to understand the underlying principles of linear motion and use the correct equation that takes into account the initial velocity. It is also helpful to double-check calculations and use real-world data to validate results.

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