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dV is the maximum amount of change your ship can do to your velocity.
It works out mathematically to acceleration * time.
dV=a*T
Your engines give off so much thrust and can only maintain that thrust if they have fuel.
Mass changes depending on how much fuel you have but you can use your ship mass at 50% fuel for any equations.
Back to your car example, if it can accelerate at 5 m/s and has 10 seconds worth of fuel, it has 50 m/s of dV.
If you drive it on a perfectly flat road and through it into neutral as soon as your fuel runs out, your car will be going 50 m/s.
Your velocity can still change if you add a hill into the mix but the total amount of energy your car has won't change.
thats what the definition says when you google it on google, but i think merriam websters definition is more clear and precise "Definition of velocity 2: the rate of change of position along a straight line with respect to time". so any quantitative distance + any quantitative time is a velocity E.g: 1-metre-per-second is a velocity, because it describes a distance (1 metre) over the course of a time (1 second), and so that time or length frame could be anything and you would have a velocity. but "fast" is not a velocity, cuz "fast" is not a quantitative.
if your going 50m/s thats still a velocity even if you havnt told as which direction your going, its still a velocity because if you are going a distance over a course of time, than thats still a velocity, because a distance has to be in a direction.
Delta V (DV) is how much you can change your velocity, not velocity its self. so if you have 300m/s of DV, you can change your velocity by 300m/s (if you have the thrusters to do so).
so say your going directly up 100m/s in a vacuum, and that you have 1 thruster pointing up, and 1 pointing down. and you have 300m/s of DV, so if you used all of your DV on 1 of the engines, you would either be going down 200m/s (100 minus 300) or you would be going up 400m/s (100 plus 300).
once you get into the second dimension the specifics of how things interact gets more complex, and even harder in the third. but that 1 dimensional example of DV will tell you what DV is, and what it does.
if you were confused by any of this, or want a better explanation on any of the specifics, or any comments at all on what i said, then make sure to ask/say them!
im gonna ask someone who knows math/physics way better than me if everything i said above is right, i will update this paragraph im writing right now after i asked them, so that you can have a better idea if what i said is correct or false.
EDIT quite a few things i said are wrong i will fix later, mainly the specifics of what i talked about with DV
If you want to raise your Ap or Pe, you'll burn prograde or retrograde to change your speed. If you want to change the inclination of your orbit, you'll burn normal or anti-normal to change your direction.
Please escuse the rough estimates from memory, but here is a practical example of dV. Let's say it takes you about 3,800 m/s dV to achieve a 100 km circular orbit around Kerbin. To raise your Ap so you'll get a Mun intercept, you'll need another 800 m/s dV. Once you get there, you might need 250 m/s dV to slow into a circular orbit around the Mun. If you're orbiting at 500 m/s, you may want 750 m/s dV to land, and 600 m/s dV to return to orbit. Then another 250 m/s dV to leave Mun orbit and get within 40 km of Kerbin. The atmosphere will slow your ship down from there so you can land. Adding that up, we get 3,800 + 800 + 250 + 750 + 600 + 250, or about 6,450 m/s dV needed for our rocket to go to the Mun and return. There are formulas and mods that let you compute your dV.
Think of DeltaV like your gas tank in a car. You could measure that gas in gallons (or liters) remaining, or you could measure that in miles (or kilometers) remaining. Delta-V is like measuring your gas tank reserve in miles, i.e distance, remaining.
DeltaV is simply a shorthand way of measuring energy in the fuel/rocket to know "how much have I got left" in a meaninful way to a rocket.
Also, as others have pointed out, the OP has velocity correct. It is a relative speed and a direction.
*Delta-V does respect the fact that the mass of the ship will reduce as fuel mass reduces. The "mass of ship" aspect simply means that delta-V will increase if you dump mass (other than existing fuel) and decrease if you add mass (other than the existing fuel on the ship).
"Velocity" is vector and describes both speed and direction. When you're driving due north at 60 miles per hour, that describes your velocity.
"Delta V" describes acceleration, or the change (in physics, "delta" means change) of velocity over time. Because velocity is a vector which also describes direction, delta V can have a direction component. When you're driving due noth at 60 miles per hour and get T-boned by a semi also going at 60 miles per hour, the delta-V is definitely going to represent a change in direction.
KSP is all about vectors, which describe both speed and direction, because getting from point A to point B depends on the direction your rocket is going at any given time.
For example, to encounter Mun from orbit of Kerbin, you point your rocket in the correct direction and fire your engines for a certain period of time (depending on the power of the engines and mass of the ship), thereby adding delta-V, or acceleration. For Minmus, you have to change direction at some point to match orbits, thereby increasing the total delta-V required for a Minmus encounter.
dV is NOT acceleration. Acceleration is change in velocity (dv) over time. That's why accelerations are measured in m/s^2 and dV is measured in m/s.
So, if I get you right. Velocity is distance over time, it doesnt need a direction. However, then what in the world is speed? And why on highways is there an "speed limit" not "velocity limit"?
Also, so what iv gathered from you all is that delta V is your potential velocity change. So back to my car, if im going 50m/s, and my car-which is the 'el cheapo' model-consumes 1m of gas per second, and my tank holds 10m of gas. Assumimg im coasting and not pressimg gas peddle, My delta V is 550m/s, right? Because thats the maximum potenial I can change my velocity. (50*10=500[my delta v if i was still at start]+50 [since I was traveling 50 at start]=550. If not, please correct me. I really appresate any help you guys give to try to teach me.
Velocity definitely needs a direction. It's a vector quantity. Speed doesn't have a direction - it's a scalar quantity. As for highway signs, the word "speed" is correct, but that's probably more about people not understanding the difference. It's like how certain groups conflate the word "theory" with "guess"
Using cars as an analog for rockets doesn't work well. Your car burns gas regardless of whether your foot is on the gas or not and if you don't hit the gas, you slow down because of friction. Also, you don't expend gas to slow down - the brake doesn't use fuel to operate. Your car also doesn't get a constant amount of "thrust" (not really thrust, of course) from the gas it burns. When the car's fuel tank is full, the car is heavier and when the tank is almost empty, the car is lighter. The lighter car goes faster burning the same amount of gas. This isn't that big a deal in cars because the fuel's mass is trivial compared to the rest of the car, but it's very important in a rocket.
Ty for velocity correction btw
dV is just the potential for your rocket to change its velocity. You can do this burning fuel, aero braking with an atmosphere or flying gravity assists. They all change your velocity. You only "pay" for changes you make with your fuel supply, hence people talking about "free dV" with areobraking.
It's useful to know your remaining dV as it tells you where, when and how quickly you can get somewhere. Take the 800m/s of dV you need to get to the Mun from LKO. If you don't have 800m/s then you cannot reach the Mun at all. If you can only spend 800m/s, you can only go at the right point in your orbit when your 800m/s burn puts you in the same bit of space as the Mun at the same time. This is a (hohmann) transfer window. For interplanetary transfers this window could only occur once a year or more. You'll get to the Mun in about 8 hours, Jool takes about 3 years by Hohmann transfer.
If you have more dV you can go to more places or fly less efficient but faster transfers more of the time. Duna is 1050m/s and 300days away by hohmann transfer. You then have to spend about 600m/s to capture for low orbit. If you go Elon Musk style and burn up 1600m/s going there and then aerocapture at Duna you can go outside the transfer window and you can get there much quicker.
My attempt at an explanation may induce more
First is the fundamental physics definition, which is that dV is a change in velocity.
Creating a manoeuvre node is a good example, it gives defined direction along with magnitude but also at a defined time which is a necessity in a constantly accelerating system.
Applying this straight into spaceflight is problematic for a couple of reasons.
First of all orbit is a state of constant acceleration, so if you don't ignore this it means that a craft in orbit has infinite dV..... which is useless info.
A constantly moving system makes varying frames of reference a necessity, and across multiple frames of reference adding a direction makes comparison difficult.
So dV in spaceflight comes in a modified form. Starting as potentials.
As people have mentioned, a crafts dV budget will give a total change in velocity that a craft can achieve. It is calulated as, listed as, and in part used as a speed, it doesn't become a velocity until it gains a direction for actual manoeuvres.
Similarly a dV map gives minimum changes in magnitude of velocity (change in speed!), with the caveat that they are used in the 'correct' (but undefined) direction and circumstances.
As a speed you can compare the crafts dV to a dV map, by adding up the dV costs of the list of manoeuvres your craft will carry out to determine if your craft has what it takes, and adjust your craft if it does not.
Its only when you actually come to the manoeuvres themselves that direction is needed, or even wanted. Once you have one then you have a true velocity.
This is wrong on a technical level as all we are given is speed, but I think understand what you mean, and its kind of relevant to what I was writing about.
In practice anything that has speed is going to have a direction, thats a fact. But speed and velocity are different concepts and are applicable to different problems. Like in the case of dV above, sometimes even if you know the velocity ommiting the direction from a problem simplifies it.
Case in point, the already mentioned speed limit signs.
A road can be considered a fixed route, and it is generally frowned upon to go backwards so it wouldn't be difficult to convert the speed limit to a velocity limit.
However as this would mean new signs would need to be added every time the road turns doing so would be extremely weird.
If you read my response carefully, you'll see that I said delta-V is, exactly as you say, change of velocity over time. You can't have a change in velocity without time going by. So, because a change of velocity necessarily always occurs over time, delta-V does indeed describe acceleration.
DeltaV, as used in rocketry, is not a measure of acceleration (except in the most pedantic sense in that application of deltaV must use some time period). A difference in V (hence delta-V) is not the same thing as acceleration.
DeltaV, as used in rocketry is a measure of the rocket's remaining "fuel level". DeltaV as used in rocketry is simply how much change in velocity is still left in the tank. You could of course measure remaining fuel in terms of mass, or volume, or even time remaining (as is sometimes the case), but delta-v is one, short hand method, for describing how "far" a given rocket can go. As mentioned by others, it is most useful when comparing to a "delta-v map" to get an idea of how capable a rocket is. A given rocket with more delta-v than a second rocket will be able to "go more places" than the rocket with less delta-v. That's it really.
In the case of rockets, and orbital mechanics, how "far" a rocket can go is not really a measure of distance, as pointed out by others, but more a measure of change in velocity. Thus, instead of measuring a rocket's "range" in miles or kilometers, a rocket's capability is often measured in delta-v (as opposed to delta-x, which would be a distance).