Acceleration Signs

by Patrick Ford
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Hey, guys. So in your motion problems, you run across this phrase speeding up or going faster, and you might take that to mean that your acceleration is positive. But be careful, because this is not always mean this. Students get this tripped up all the time. So in this video, I'm gonna show you how the acceleration, sign effects, velocity and speed. I'm gonna show you really, really simple way to think about this. Let's check it out. So guys, again positive acceleration does not mean speeding up or going faster. Positive. Accelerating positive acceleration literally just means that your velocity is becoming mawr positive. On the other hand, negative acceleration just means that your velocity is becoming mawr negative. We could just see this from the example. I'm sorry for the equation. We know the acceleration is delta view over Delta T. So positive acceleration means that the change in velocity is positive, a k a. Your velocity becoming more positive. And the negative acceleration means that your velocity is becoming more negative. That just comes from the equation. Let me just show you a bunch of examples to see how this works and where the confusion comes from, so you don't make the same mistakes yourself. So we have all these problems here, we're gonna indicate whether the acceleration is positive or negative. And if speed is increasing or decreasing, we're gonna assume Delta T is for So let's get Let's just get to it. We've got V not equals 10 v Final equals 30. So I'm just drawing a quick little sketch. Here's my V Knots, which is 10. Then at some later time from here to here. I know that my final velocity is gonna be a bigger vector, and this is gonna be 30. So to calculate the acceleration, I need Delta be over Delta T. So my change of velocity is 30 minus 10. That's my initial divided by Delta T, which is four. So this is 20/4, and I get 5 m per second squared. So notice how this is a positive number. That's my acceleration. So that's positive. What about the speed? Well, whenever you think about the speed, it just think of the number of the velocity, the magnitude of velocity, not the actual sign. So I'm going from 10. That's the number 2 30 which is a bigger number again. Forget about the sign, which means that my speed is increasing. Let's take a look at part B. Now I have a velocity that's negative. And a final velocity. That's negative. So I'm actually gonna start going to the left. So this is my initial velocity here. Ivy not is negative. 10. And then my final velocity over here is gonna be negative. 30. I know that this is this Takes some time, which is Delta t. So to calculate my acceleration I need Delta V over Delta T My delta V is gonna be negative. 30. That's my final minus my initial negative. 10. Be careful with signs on Delta T is for so this actually negative. 20/4. So this is actually negative. 5 m per second squared. So my accelerations Negative. So this is my acceleration over here. What about the speed? Well, again, Just think about the number, not the sign. Just think about the magnitude of your velocity. I'm going from negative 10. So the number is 10 to negative 30. The number is 30. The number gets bigger. Forget about the sign. So that means my speed is increasing. So notice how one situation. My acceleration was positive. My speed was increasing, and in the other situation, my my acceleration was negative, but I was still speeding up and my speed was still increasing. So speeding up just means that you're going faster. And that means that the magnitude of your velocity just think of the number is increasing. And so the easiest way to think about this is if you're acceleration and your initial velocity are in the same sign, have the same sign. That's when your speed increases. For example, here my acceleration was positive. My initial velocity was positive, so my speed increased over here. My acceleration was negative. My initial velocity was negative. And so my speed increases. Well, let's take a look. More more problems. So here we've gotten a velocity of 30 and a final velocity of 10. So here, now I've got my initial velocity is 30 and then my final velocity is gonna be 10 over here. So I'm gonna drop my little interval from here to here. Now I just calculate the acceleration. A equals Delta V over Delta t my Delta V. Now my final velocities. 10. My initial velocity is 30 and my time is four. So this is gonna be negative. 20. And this is gonna be four. So I get an acceleration of negative 5 m per second squared. So my acceleration is negative. What about the speed again? Think about the number first. I'm going from 30 and now I'm going to tend. The number is getting smaller this time, so my speed is actually decreasing. Let's go. The last one negative. 32. Negative. 10. So here what happens is first I'm going. This is my vision on its negative. 30. Draw it again. Negative. 30 over here. And then finally it's gonna be negative. 10. And then my interval is over here. I know. That's four seconds. So what's my acceleration? So acceleration. Delta V over Delta t. So my Delta V, what's my final velocity? It's negative. 10. My initial velocity. Negative. 30 again. Keep track of all the signs over four. So this becomes positive. Positive. This becomes 20/4 and that's just 5 m per second squared. It's positive. So here we got a positive acceleration. What about the speed? Speed is going from 30 to 10. The number just forget about the sign. The number is going from 30 to 10 which means that my speed is actually decreasing here. So again now we have a situation where we have negative acceleration and decreasing speed. But positive acceleration could also mean decreasing speed So slow slowing down just means that obviously you're going slower. Which means that the magnitude of your velocity is decreasing and this happens whenever you're acceleration and your initial velocity actually have the opposite signs. So for example, here my acceleration was negative. Positive initial velocity. So I slowed down here. My acceleration was positive. Initial velocity was negative. And so that means I'm also slowing down. Alright, guys, hopefully it's sort of like illustrates where that confusion comes from. And so hopefully these these rules here give you a better understanding of what the relationship between signs of acceleration and velocity are. Alright, I got this one last problem here. Let's just get to it. We've got the driver of a truck that is moving to the left of 30 m per second, slows down by taking their foot off the pedal and basically we're gonna calculate the magnitude and direction of the acceleration and it's assumed constant. So we're actually just gonna use our normal steps for solving motion problems with acceleration. So let's just get to it. Let's just draw a quick little sketch here. Eso I've got this truck that's moving to the left. So here I got this truck that's moving to the left. We know that this initial velocity here is gonna be 30 m per second, but if it's moving to the left, it's actually going to be a negative. And so we're told that the truck comes to a stop after traveling 150 m. So basically, after some distance over here, which we know Delta X is gonna be negative 150. Now, at this point here, the final velocity is going to be zero. But again, this is negative because we're moving to the left. So we need three out of five variables. Let's just go ahead and list them out. I need Delta X. I need V not V a n t. I know. Delta X is negative. 1 50. I know my initial velocity is negative. 30. My final velocity is zero. And then my acceleration is what I'm looking for this is my target variable. And then, um yeah, so I've got my diagram, and I've got my five variables. I've got the known variables and what my target variables are. So now I just have to pick the, um, equation that does not have my ignored one. So these are my three variables that I know I'm looking for the acceleration and the time is gonna be my ignored variable. So if you look through our list of equations here, the one that doesn't include time is actually gonna be the second one over here. So we're gonna use equation number two. Whoops. So the the final squared equals the initial squared plus to a times Delta X. And so we're looking for this acceleration. Over here, we know that my final velocity is going to be +00 squared. My initial velocity is gonna be negative. 30 but it's squared and then plus two eight times Delta X. So I get zero equals this into being 900 plus two times a times my delta X, which is negative 150. So this ends up being when I move this to the other side to get negative. 900 equals on. Then what? I multiply too. And the negative 1 50. This becomes negative 300 times a and so all I have to do now is divide and basically my A is going to be 900 over 300 which is just 3 m per second. What about the sign? Well, now my sign is positive. It's a positive 3 m per second, but notice how everything in my diagram here was negative. So even though I was slowing down by taking my foot off the pedal, my acceleration was actually positive. And that's because everything in my diagram was pointing to the left. Alright, guys, that's it for this one. Hopefully, this sort of clears up some of the confusion. Let me know if you have any questions.