# The d in Newton's second law of motion?

1. May 29, 2009

### ScienceNerd36

the "d" in Newton's second law of motion?

Hello there my fellow quantum inquisitors.

I was just over in the physics forums library and was wondering what the "d" in the equations of Newton's second law of motion means?

ScienceNerd36.

2. May 29, 2009

### Blenton

Re: the "d" in Newton's second law of motion?

If what you mean is "F = d(mv)/dt" then the d/dt refers to the derivative of mv, or the change of mv "d(mv)" over time "dt". Once you learn calculus it'll make sense.

3. May 29, 2009

### Cyosis

Re: the "d" in Newton's second law of motion?

To add to what Blenton said.

You probably know that if you have a function v(t), speed as a function of time, and you want to find the average acceleration between two points you calculate $$\frac{v_2-v_1}{t_2-t_1}=\frac{\Delta v}{\Delta t}$$. Is this familiar? If you want to find the instantaneous acceleration that is the acceleration at a time t the gap between t2 and t1 becomes very small (goes to zero). When you do this the deltas are replaced by ds and the result is $$a(t)=\frac{dv(t)}{dt}$$. Once you get some calculus you will get to know how to use this operation.

We can also execute this operation multiple times. You know that the average velocity is given by $$\frac{\Delta x}{\Delta t}$$. If $$\Delta t$$ becomes very small (goes to zero) we write it as $$v(t)=\frac{dx(t)}{dt}$$. If we want to find the acceleration now we can use our previous expression $$a(t)=\frac{d}{dt} \frac{dx(t)}{dt}=\frac{d^2 x(t)}{dt^2}$$. Therefore Newton's second law can be written as.

$$F=ma=m\frac{dv}{dt}=m\frac{d^2x}{dt^2}$$

4. May 29, 2009

### ScienceNerd36

Re: the "d" in Newton's second law of motion?

Thanks for the help. Now if you could just teach me calculus.

5. May 29, 2009

### Cyosis

Re: the "d" in Newton's second law of motion?

Check this out http://en.wikipedia.org/wiki/Derivative. I assume you've had geometry to some extent. If you know what a tangent line/slope is then you should be able to figure out the definition of the derivative.

6. May 29, 2009

### Kurdt

Staff Emeritus
Last edited: May 29, 2009
7. May 29, 2009

### Staff: Mentor

Re: the "d" in Newton's second law of motion?

Um, there are whole textbooks about the subject.

8. May 30, 2009

### ScienceNerd36

Re: the "d" in Newton's second law of motion?

Can calculus be learned from text books alone?

9. May 30, 2009

### HallsofIvy

Re: the "d" in Newton's second law of motion?

Yes, though it is not easy and I wouldn't recommend it.

10. May 30, 2009

### Dr.D

Re: the "d" in Newton's second law of motion?

Newton and Liebnitz each learned it without a book.

11. May 30, 2009

### mabs239

Re: the "d" in Newton's second law of motion?

Finding the area of a circle helped me learn calculus.

12. May 31, 2009

### ScienceNerd36

Re: the "d" in Newton's second law of motion?

Any books ye would recommend?

13. May 31, 2009

### Majcah

Re: the "d" in Newton's second law of motion?

Calculus is the math of change. The "d" in the equation is just telling you that there is a change in velocity over a change in time. If a change in position over a change in time gives you velocity, then a change in velocity over a change in time will give you acceleration. This yields Newton's second law F=ma where the "m" is a mass that is constant. Calculus will expand upon this further, but you don't really need to know it to understand what the "d" means.

14. May 31, 2009

### ScienceNerd36

Re: the "d" in Newton's second law of motion?

Thanks, but I would still like to know a bit more about calculus. Are there any books like "Calculus For Dummies" or "How To Learn Calculus In 7 Days" that anybody would recommend?

15. May 31, 2009

### Majcah

Re: the "d" in Newton's second law of motion?

The "dummies" series probably has something on calculus that might be basic enough to give you some insight. If it follows the same format as "Physics for dummies" then most likely it will give you a very watered down version of calculus. In the end it just depends on what you want to get out of it.

16. May 31, 2009

### tiny-tim

Hi ScienceNerd36!
:rofl: :rofl:

Best not to try to learn calculus before you have to.

For the time being, read d as "rate of" …

so dv/dt = rate of v over rate of t …

in other words, if you draw a graph of v against t, then at any point on the curve,dv/dt is the rate at which v increases divided by the rate at which t increases (which equals the slope of the curve).

17. May 31, 2009

### mikelepore

Re: the "d" in Newton's second law of motion?

Schaum's Outline series. As little of the philosophical yackety-yack as possible. Just -- here's a certain type of problem, here's how you do it, look at the example, now you try a few, then look up the answers to see if you did them right ... next topic: here's another type of problem...

18. Jun 1, 2009

### dE_logics

Re: the "d" in Newton's second law of motion?

I personally had a very bad time learning calculus and I still don't know it...it's in chaos.

Its good if you get an e-book.

19. Jun 1, 2009

### ScienceNerd36

Re: the "d" in Newton's second law of motion?

This has all been a lot of help to me. I really appreciate all of you putting in the time to answer my questions. See you on another thread.

Yours faithfully,
The Calculating ScienceNerd36.

20. Jun 1, 2009

### vanesch

Staff Emeritus
Re: the "d" in Newton's second law of motion?

Just to add something: in fact, Newton INVENTED calculus all by himself IN ORDER to be able to write his laws! It is because he desperately needed this tool in order to formulate what he wanted to say, that he invented calculus.

It is because he "needed that d there" (but that was not his notiation, btw, that's Leibniz who invented it, independently of Newton), that he invented calculus.

(Ok, this is a simplification of the historical record which is more involved, but it is not very far from the essence).