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

## Main Question or Discussion Point

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.

## Answers and Replies

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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.

Cyosis
Homework Helper

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.

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

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

Cyosis
Homework Helper

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.

Kurdt
Staff Emeritus
Gold Member
Last edited:
jtbell
Mentor

Now if you could just teach me calculus.
Um, there are whole textbooks about the subject.

Can calculus be learned from text books alone?

HallsofIvy
Homework Helper

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

Newton and Liebnitz each learned it without a book.

Finding the area of a circle helped me learn calculus.

Any books ye would recommend?

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.

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?

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.

tiny-tim
Homework Helper
Hi ScienceNerd36!
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?
Thanks for the help. Now if you could just teach me calculus.
: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).

Are there any books like "Calculus For Dummies" or "How To Learn Calculus In 7 Days" that anybody would recommend?
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...

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.

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.

vanesch
Staff Emeritus