# Resistance force changing the velocity of an object

• highschoolstudent454
highschoolstudent454
Mentor note: Moved from a technical section, so is missing the homework template.
A Body of mass 1kg moves with a uniform velocity of magnitude 12m/s, a resistance of force of magnitude 6x^2 (newton) where x is the displacement (meter) which the body travels under the action of the resistance acts on it.
1) Find the work done by the resistance until x=4
2) Find the velocity of the body and its kinetic energy at x=2

I have no problem in solving the question. However, I have some difficulty in describing motion over the change of x. I got the kinetic energy to be T = 72 - 2x^3 (after integrating with respect to x). Does this mean that the body will stop at x = 36^(1/3) < 4 as all initial kinetic energy will be consumed or will the body move in the opposite direction in the direction of the acting resistance? in other words, will the body continue to move in the opposite direction or stop, and thus the first requirement would be meaningless?

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highschoolstudent454 said:
Mentor note: Moved from a technical section, so is missing the homework template.
A Body of mass 1kg moves with a uniform velocity of magnitude 12m/s, a resistance of force of magnitude 6x^2 (newton) where x is the displacement (meter) which the body travels under the action of the resistance acts on it.
1) Find the work done by the resistance until x=4
2) Find the velocity of the body and its kinetic energy at x=2

I have no problem in solving the question. However, I have some difficulty in describing motion over the change of x. I got the kinetic energy to be T = 72 - 2x^3 (after integrating with respect to x). Does this mean that the body will stop at x = 36^(1/3) < 4 as all initial kinetic energy will be consumed or will the body move in the opposite direction in the direction of the acting resistance? in other words, will the body continue to move in the opposite direction or stop, and thus the first requirement would be meaningless?
Since the object is moving at a constant velocity, its net acceleration must be zero. It's given that there is a force that resists motion, so what can you deduce?

The statement of the problem specifies that the velocity is "uniform". This means that it is the same at x = 2 (2 what?) as it is at x = 4. Is that really the case, or do we have translation issues? Why do you think the body will stop?

Welcome, @highschoolstudent454 !

It seems to me that the problem is not specific about the nature of that resistive force.
It could be movement dependent (like in brakes of a car), or not (like in the reversed thrust of a landing airplane).

It also seems to be peculiar that the nature and location of x=0 is not indicated (perhaps the point at which the resistive force begins to act on the body that has been moving at uniform velocity?)

Lnewqban said:
It also seems to be peculiar that the nature and location of x=0 is not indicated (perhaps the point at which the resistive force begins to act on the body that has been moving at uniform velocity?)
Yes, I see two interpretations
1. The body moves initially at uniform velocity, i.e. no force acts on it, until it reaches x = 0 where a resistive force causes it to lose speed.
2. The body is moving with uniform velocity from x = 0 to x = 4 while the resistive force acts on it.

I suspect that the statement of the problem was translated by OP from a non-English language.

Lnewqban

Hey everyone, This is the school book's answer to this question. I think -like kuruman said- it initially considered the body to be moving with a uniform velocity and then a resistance force acted on it.
As I have stated earlier I have no problem with those calculations. My issue is if we try to find a formula to describe the kinetic energy of the body at any x, T = 72 - 2x^3, plugging for x=4 will give negative T is this even possible?
to Lnewqban and kuruman,
I wrote the question above in my first post in Bold as it was written letter by letter in my book (Dynamics High school Egyptian book). I have heard some talk that this book borrows questions and explanations from different resources. One more thing: The book is translated from the Arabic version - the predominant version in Egypt. I hope these notes clarify the question. Thanks in advance.

SammyS
kuruman, I got your point. Is it reasonable to find the work done by resistance at x=4 while the object won't reach this displacement?

From the solution one may conclude that
(A) to answer question 1 one must assume that the body is moving with uniform speed 12 m/s from x = 0 m to x = 4 m.
(B) to answer question 2 one must assume that body is moving with speed 12 m/s with no forces acting on it until it reaches x = 0 where the resistive force only acts on it.

The premises to each question are different and this is not apparent in the statement of the problem that you posted. What does the Arabic version say?

highschoolstudent454

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