# Real life situation to a sin graph on position by time graph

#### Skhandelwal

Here is the deal, no matter how many times you take the derivative of the sin graph, you never get zero b/c you get in a cycle, well, I just can't picture anything like that happening in real life b/c if you keep taking derivative, at some point of time, the graph has to be y=0 equation b/c the acceleration of the acceleration of the.... has to be at some point of time be zero. Do you follow me?

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#### CRGreathouse

Homework Helper
Why? Suppose you were pacing, moving from -1 to 1 and back, following the value of the sine function.

#### HallsofIvy

Homework Helper
Skhandelwal said:
Here is the deal, no matter how many times you take the derivative of the sin graph, you never get zero b/c you get in a cycle, well, I just can't picture anything like that happening in real life b/c if you keep taking derivative, at some point of time, the graph has to be y=0 equation b/c the acceleration of the acceleration of the.... has to be at some point of time be zero. Do you follow me?
It's not clear what you are asking. Yes, the repeated derivatives of sin x, like the derivatives of most functions, are never identically 0. But then you say "has to be at some point of time zero". Are you saying that for some t some derivative must be 0? Yes, that's true for sin t. The first derivative of sin t is cox t which is 0 for x= any odd multiple of $\frac{\pi}{2}$.

On the other hand, the function y(x)= ex has derivatives of all orders equal to ex which is never 0 for any x.
It's not clear to me what you are saying "has to be at some point of time zero".

#### Skhandelwal

Yes, you can add exponential function too. All I am asking is that when you take derivative of position graph, you get velocity, you take derivative of velocity graph, you get acceleration, you take deriv. of accel. graph, you get jerk(accel. of accel.), you take deriv. of that(you get accel. of accel. of accel.) and as you keep taking deriv. you keep getting accel. of accel. of ...
Now the thing is, in real life, I cant think of any situation that would project such a phenomenon. In physics class, life motion can be presented by position graph, well I just cant think of any situation where the rate at which you accelerate accelerates at the same rate. Do you follow me this time?

#### Office_Shredder

Staff Emeritus
Gold Member
Population growth accelerates exponentially.

A mass bouncing on a spring moves with harmonic motion.

There's your sine and ex models

#### Skhandelwal

I get sin/cosine problem, however, exponential problem remains...

For the exponential graph, if I try to explain you my question mathematically, it will take a whole page for me so I will ask you conceptually. I realize that our population growth is increasing exponentially, but if we try find the acceleration of the acceleration of rate it is increasing at, we won't get the same graph no matter at what rate something is increasing.(as far as I know which has to be wrong if there is an example of e^x graph) What I am wondering is that how can there be graph whose derivative is the same graph as so on till infinity correspond to a real life situation?

Here is a summarized version of the mathematical version of my exponential problem question. If something is growing at an exponential rate and its function is given as y=2^x then its derivative will be 2^x X Ln2. Which is less and that makes sense, although no matter how many deriv you take of that it will never be zero, I understand that. But what I am wondering is that can there be a real life situation who function will be given as y=e^x? So no matter how many deriv. you take of it, you will get the same thing?

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