# What's the difference between Δ and d in physics ?

1. Mar 28, 2016

### Peter25samaha

Is the acceleration : a=Δv/Δt equivalent to a=dv/dt ??
Anx whats the difference between Δ and d and can i use Δ when i want ?
a=d2x / dt2
Can we write the same using Δ ?

Last edited by a moderator: Mar 28, 2016
2. Mar 28, 2016

### PeroK

$\Delta$ usually represents a finite change in something. So, technically:

Average Acceleration = $\frac{\Delta v}{\Delta t}$

Where $\Delta t$ is some finite (not necessarily small) period of time.

$a = \frac{dv}{dt}$ denotes the derivative of velocity with respect to time. This gives the instantaneous acceleration.

The two are related by:

$\frac{dv}{dt} = \lim_{\Delta t \rightarrow 0} \frac{\Delta v}{\Delta t}$

3. Mar 28, 2016

### Peter25samaha

a=d2x/dt2 and here what does it mean the : d2x
Shoudn't be :dx2 ?

4. Mar 28, 2016

### PeroK

$\frac{d^2x}{dt^2} = \frac{d}{dt}(\frac{dx}{dt}) = \frac{dv}{dt}$

The notation is probably because you can view $\frac{d}{dt}$ as the differential operator, hence $\frac{d}{dt}\frac{d}{dt} = \frac{d^2}{dt^2}$ but I wouldn't read too much into the notation. Other notations for acceleration include:

$x''$ and $\ddot{x}$

5. Mar 28, 2016

### Staff: Mentor

These will have identical values if velocity vs. time graph is a straight line (around the region of interest), otherwise Δv/Δt is an approximation to the exact slope of the tangent, dv/dt.

6. Mar 28, 2016

### SteamKing

Staff Emeritus
The trouble you are having is this is calculus notation. If you haven't studied calculus yet, you're going to be understandably confused.

7. Mar 28, 2016

### Peter25samaha

Yes and if i am using a 3D graph with x y and z i will put vector on each one and i have to write it like this : dv/dt right ?

8. Mar 28, 2016

### Peter25samaha

Okay but this :
a=d2x/dt2
Can be equal to delta squared if velocity and time graph is a straight light ?
a=Δ2x/dt2
Those two acceleration are equal ?

9. Mar 29, 2016

### SteamKing

Staff Emeritus
Generally, one doesn't mix Δ and d notation in the same expression.

10. Mar 29, 2016

### PeroK

First $\Delta^2$ has no obvious meaning that I can see. $(\Delta x)^2$ has the obvious meaning.

Second, as Steam King points out, $\frac{\Delta}{d}$ is meaningless.

Third, you should be able to see for yourself why $a \ne \frac{(\Delta x)^2}{(\Delta t)^2}$

More generally, you seem to be just groping in the dark here. You seem to be struggling to understand what is going on with time and distance and motion. This material should make sense. Are you learning calculus?

11. Mar 29, 2016

### Peter25samaha

Yes i am learning but i only want to know when i use d and when i use Δ if i have to calculate the velocity or acceleration

12. Mar 29, 2016

### PeroK

Hopefully that was answered in post #2.

13. Mar 29, 2016

### Peter25samaha

Okay sorry i havent seen this

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