How do I solve this differential equation: dx/dt = 3 m/s for x(t)?

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In summary, the conversation is about a middle-aged person who graduated in 1986 with limited knowledge in calculus. They were given a problem by a resident and are struggling to solve it. The problem involves a differential equation and the person is seeking help to solve it. The solution is provided in the conversation.
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ct fisher
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Hello out there,and pardon my dementia but:

I am a middle aged guy, bordering well on old now, who graduated from professional school in 1986 and I was already an older than most student at that time. I had one semester of calculus in 1973 and slipped through with a C major.
My calculus is limited to very basic diff and integ and a young upstart resident handed me this today:

dx/dt = 3 m/s solve for x(t)

I am lost. The answer is not zero or some constant I am sure. The two variable business changes everything, right?

If this is a differential equation, nothing in my old notes is helping to enlighten me. Any help would be appreciated.
If this upstart resident has made a fool of me and the problem is bogus, he will regret it. He says he could not answer it so I don't know what is up his sleeve. I'm thinking that the problem may be just a lot of bull.Thank you. CTF
 
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  • #2
I will bite.

Integrate both sides to obtain:

[tex]\int_{x'=0}^{x} dx' = \int_{t'=0}^{t} 3 dt'[/tex]

That is, [tex] x' |_{0}^{x} = 3 t' |_{0}^{t} \implies x(t) = 3t[/tex].

Edit: I post this full solution because I believe the question is simple enough that there's no point beating around the bush.
 

FAQ: How do I solve this differential equation: dx/dt = 3 m/s for x(t)?

What does "Dx/dt = 3 m/s" mean?

The notation Dx/dt represents the derivative of the position function x(t) with respect to time. In this case, it means that the position of an object is changing at a rate of 3 meters per second.

What is the significance of the "3 m/s" in the equation?

The "3 m/s" represents the instantaneous velocity of the object at any given time. It tells us how fast the object is moving at that specific moment.

How do I solve for x(t) in this equation?

To solve for x(t), you will need to integrate both sides of the equation with respect to time. This will give you the position function x(t) in terms of time.

Can this equation be used to predict the position of an object at a specific time?

Yes, once you have solved for x(t), you can plug in a specific time value and find the corresponding position of the object at that time.

What other factors may affect the position of an object besides velocity?

Other factors that may affect the position of an object include acceleration, initial position, and external forces such as gravity or friction. These factors can be incorporated into the equation to create a more accurate model of the object's motion.

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