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Intro to Velocity and Speed

Patrick Ford
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Hey guys in previous videos, we talked about the difference between distance and displacement to describe how far something moves. And in this video we're gonna talk about another pair of important but related words called velocity and speed. Let's check it out. So let's take a look at a familiar example, let's say we were moving from A to B and then back to C. Again, we know that this is 10 m to the right and we're going to move six m and then we're gonna be moving to the left here, there was two words to describe how far something moves. That was distance, which remember was given by the letter D. And was a scalar your distance just with the total of everything that you travel 10 and six. So we know this is just 10 and six and that makes 16 The displacement on the other hand, was a vector and it's the difference between where you started and where you ended and it was the shortest path between those two points. And we know that your final position is for your initial position is zero. So your displacement, which is just 4 0, was just 4m to the right. So just like distance versus displacement, there's two words to describe how fast something is moving. And the basic idea here guys, the main idea is that speed is related to the distance that you travel, whereas velocity is related to the displacement that's traveled. Let's take a look. So for the equations, speed is going to be s and it's defined as the distance over time. Whereas velocity is defined by the letter V. And it's defined as the displacement over time. So for the equations, the speed is gonna be distance over time, D over delta T. Whereas velocity is gonna be delta X. The displacement over delta T. And they're both given in terms of units of meters per second, that's gonna be the units that were working with over here. So let's take a look. So we've got that this distance here, the distance remember is going to be a scalar which means that the speed is also going to be a scalar. If this is a scalar then that means that this is going to be a scalar. Now on the other hand, the displacement was a vector. And if the velocity displacement over time and that means that velocity is also going to be a vector. So scalar for speed and vector for velocity. Now let's talk about the signs now, for speed, the speed is always going to be either positive or zero because it depends on the distance and the distance can always just be positive or zero, it can never be negative, whereas the displacement can be positive negative or zero. So your velocity can be positive negative Or zero because that's what your displacement can be. And so let's talk about negative velocity for a second, what does negative velocity mean? Remember signs in physics just have to do with directions. So negative just means that you're moving in the opposite to whatever the positive direction is and your problem is gonna tell you what that direction is. So for example, let's say the right direction is positive, anything moving to the left is going to be negative, and sometimes in rare occasions you might see that the left direction is positive. Your problem will tell you this, in which case anything that's moving to the right is going to be negative. So just means whatever your problem tells you the positive direction is anything moving to the opposite of that is gonna be negative velocity. Alright guys, that's really all there is to it. So let's check, let's take a look at an example, we're gonna jog 15 m in two seconds, then nine m backwards in another two seconds. Let's calculate the speed and velocity. So let's just draw a quick little diagram of what's going on here. So I'm gonna move, I know this is going to be 15 m in this direction, and then I'm gonna move 9m backwards in another two seconds. So this is gonna be 9m like this. So I know that the time here is going to be two seconds and the time here is also gonna be another two seconds. So let's say this part, a the speed is going to be, remember the formula we're gonna use is the distance over delta T. That's the equation that we have right up there. So we're gonna use distance over time. Now, we just have to figure out the distance for the total trip. So what's the total distance? Will we move 15 m forward and then 19 m backwards? So your total distance is gonna be 15 plus nine m and your total time, is that two seconds or no? Because remember this is two seconds for the forward direction and in two seconds for the backwards direction. So our total time is two plus two. And so what we get is 24 divided by four. So that means our speed was six m per second. What about our velocity velocity member is delta X over delta T. For the whole trip. So now what happens is we need to figure out what's the shortest path from initial to final. So just in the same way that we did the example above this is A. And B. And this is see the shortest path between initial and final is actually gonna be from here to here. So this is my displacement, this is gonna be delta X. And what is delta X. Delta X is 15 m forwards and nine m backwards. So we can do 15 minus nine over here. And then that just gives us six m. So our displacement is actually 15 minus 9/ plus two, which is the total time. So we're gonna get 6/2. And what we actually get is uh whoops, that's equals, I'm sorry, 6/4, whoops. And so we get is 1.5 m/s. Now, we have to specify a direction because we've got a positive number here. That makes sense because our displacement also points to the right, so that means our velocity vector also points to the right. That's it for this one, guys, this is the speed and velocity. And let me know if you guys have any questions.