Understanding dv/dt: A Beginner's Guide to Calculus Concepts

[ChiragGupta]

I am new to Calculus and not exactly sure what this means. Any help explaining it would be greatly appreciated. :)

 

[anorlunda]

It means the rate of change of v with respect to t. We also call it the derivative of v with respect to t.

For example, if v is velocity and t is time, the rate of change of velocity with respect to time. That is something we call acceleration.

Calculus studies go deeply into derivatives and integrals. Stick with your textbook and your lectures, and you'll understand much better. Asking questions on the Internet is not the best way to learn.

 

[jtbell]

The first few sections of this Wikipedia page may be helpful if you don't have a calculus textbook. Note particularly the relationship between the derivative and the slope of a (tangent) line on a graph (in your case, a graph of v versus t).

https://en.wikipedia.org/wiki/Derivative

But as anorlunda said, if you want to learn this stuff seriously, you really need to use a decent textbook. Asking questions to clarify specific points is fine, but learning something from scratch by asking questions one at a time is rather a hit-or-miss process.

 

[sophiecentaur]

If you want to learn how to play the piano, you don't start with the sheet music for a Chopin Prelude; you need to learn the basics first. You need to approach Calculus in the same way. Differential Calculus is actually pretty reasonable to get hold of if you already know the rules of Algebraic manipulation and stick to them.

 

[Kaura]

Calculus deals a lot with relationships of change. In the case of dv/dt v is one variable and t is another. Typically t is the independent variable and v is the dependent variable. You may be familiar with ratios of change in quantities. For example if I wanted to find my average velocity (change in distance over change in time) I would take the distance I traveled and divide it by the time elapsed. You could also do this with velocity to find acceleration which is change in velocity over change in time. Calculus takes this a step further by finding the instantaneous rate of change. Essentially the dv/dt differs from v/t due to the fact that dv/dt uses an infinitely small increment in velocity and time to find the instantaneous rate of change.

 

[sophiecentaur]

Calculus deals a lot with relationships of change

It can deal with other relationships too - such as the slope of ground or the behaviour of an object as it is deformed by a force.
When you get into differential calculus seriously you find the concept of a "limit" of the slope of a curve as the distance that the slope is measured over approaches zero. IT aims to give the slope of the tangent to a curve rather than just the gradient of a line (cord) between two points on the curve.
'Limits' is the buzz word of calculus.