Your thinking is correct but you mathematics is wrong smile

This means that a does not equal dv. It means that a = dv/dt.

Close but not quite if you are using the differential form the it isn't "a" it's "da" or the differential acceleration so

da = dv/dt.

Remember whatever you do to one side of an equation in mathematics you must do to the other.

You took the differential of the right side then you must also take the differential of the left.

You also need to use care da, dv and dt are all averages if we assume uniform acceleration

dv is actually the average velocity between two differential points dvf (the final velocity) and dvi (the initial velocity). Fortunately time is constant.

Let me write the equations showing the averages

dv (average) = (dvf-dvi)/2

dt (average) = dt

da (average) = dv (average)/dt (average)

Edited by Orac (03/02/16 06:20 AM)
I believe in "Evil, Bad, Ungodly fantasy science and maths", so I am undoubtedly wrong to you.