- #1

Trying2Learn

- 375

- 57

- TL;DR Summary
- splitting the differential

In an introductory dynamics textbook, we often see this progression

v = ds/dt ---> dt = ds/v

a = dv/dt ---> dt = dv/a

Equating the dt, we get: vdv=ads

Now my question

On the one hand, this works for certain problems.

On the other hand, this is splitting the differential.

Could someone please explain

Why it works under certain conditions? How engineers get away with this?

If it is poor math to do this: why? Is it because one should never split the differential?

How can engineers get away with this?

I see that it does work, but only in ONE dimension.

This whole issue has always bothered me but I cannot state, with clarity, conviction, precision:

Why it is poor math to do this

Why we can get away with it.

v = ds/dt ---> dt = ds/v

a = dv/dt ---> dt = dv/a

Equating the dt, we get: vdv=ads

Now my question

On the one hand, this works for certain problems.

On the other hand, this is splitting the differential.

Could someone please explain

Why it works under certain conditions? How engineers get away with this?

If it is poor math to do this: why? Is it because one should never split the differential?

How can engineers get away with this?

I see that it does work, but only in ONE dimension.

This whole issue has always bothered me but I cannot state, with clarity, conviction, precision:

Why it is poor math to do this

Why we can get away with it.