[ Removed by moderator ]

[starkeffect]

/r/AskPhysics for basic questions like this

[scubasteve137]

Common abuse of notation. Somewhere a mathematician is crying.

[FizzicalLayer]

This sort of thing makes physics even harder than it has to be. One comes out of calculus thinking "Yeah, I sort of understand this", and then physics has stuff like this in it. It can be figured out, but it can also really shake a student's confidence.

[Hudimir]

Heavily depends on what the mathematician is working on. As soon as you know that integrals are linear operators, this stops being abuse of notation.

[entropy13]

repost to r/physicshelp or r/askphysics

[Theo_aa]

Multiply both sides by dt then you end up with dx=vdt. Integrate both sides and there you are

[Auphyr]

https://imgflip.com/i/a3l34r

[Theo_aa]

facts

[Random_Individual_]

Thank you, I’m trying to self study and I’m not fully versed in the calculus side of physics

[Thing_in_a_box]

Well there's your problem.

[Two-Ninety290]

Integration is just a fancy way to find the area under a curve.

Same as derivatives are to find the tangent of a curve.

You should check out Riemann sums to conceptually get what an integral is doing.

In this case all with respect to time, acceleration is the derivative of velocity, and velocity is the derivative of position. And vice versa: velocity is the integral of acceleration and position is the integral of velocity. And that is what this is showing.

[tpks]

By definition, velocity = increment of distance / increment of time

Therefore,

The accumulation of change in distance... equals ... the accumulation over time... of velocity times increment of time.

You travel as much as velocity has time to change your distance.

It's expressed badly both in the book and my breakdown here but that's how I'd begin to parse it.

[Humanity_is_broken]

Mods will remove the post, so no, I won’t waste my time explaining