A Basic Acceleration Example Problem and Understanding Acceleration Direction

Bo: Hey guys, Billy, Hey Bo, Bobby Hi Bo lyrics, Flipping Physics, Mr P, Ladies and gentlepeople. The bell has rung, therefore class has begun.

Therefore, you should be seated in your seat, ready and excited to do a basic example problem about acceleration and to understand a little bit about the direction for acceleration Bo Ready Bobby Set Billy Go Mr P.

Okay, here we go Billy.

Please read the problem.

Billy, Mr P is riding his bike at 14 3 kilometers per hour when he begins pedalling the bike to cause a constant acceleration.

If, after 6 4 seconds, the bike is moving at 23 7 kilometers per hour.

What was the acceleration of the bike Bobby Uh? Can you show that again, please That happened pretty fast, Mr P, For you Bobby yes Great Now let’s translate the problem to physics Billy.

If you could, please read again and Bo, could you please do the translation Billy? Mr P is riding his bike at 14 3 kilometers per hour when he begins pedaling Bo.

Please stop.

The velocity initial is 14 3 kilometers per hour. Billy Pedaling the bike to cause a constant acceleration If, after 6 4 seconds, the bike is moving at 23 7 kilometers per hour.

What was the acceleration of the bike Bo? The change in time is 6 4 seconds.

The final velocity is 23 7 kilometers per hour and acceleration equals question mark, because acceleration is what we’re trying to find Mr P Bobby what next Bobby.

Well, we learned last time that kilometers per hour and seconds don’t match very well.

So let’s convert both of the velocities to meters per second.

We know there are 3 600 seconds in an hour, so multiply both velocities by 1 hour over 3 600 seconds to cancel out the hours.

We also know that there are 1 000 meters in 1 kilometer, so multipy, both velocities by 1000 meters over 1 meter to cancel out the kilometers.

Mr P, What do we get then for numbers for velocity initial and velocity final Bobby? I actually have both answers.

The initial velocity is 3 972 and the 2 is repeating, and the final velocity is 6 583, with a repeating 3, Mr P, Great Bo.

What should we do now? Bo Again? We start with the equation: Billy Bobby The equation Bo. Yes, the equation Acceleration equals the change in velocity over the change in time where the change in velocity is equal to velocity final minus velocity initial.

Once we have the whole equation written down, we can just plug in all the numbers, because we have the numbers and we get 6 5833333 minus a 3 9722222 That whole quantity divided by 6.

4.

Mr P, Yes, it is that simple, and what do we get for numbers Bobby That worked out to be 0 4079861 with 2 sig figs? That would be 0 41 meters per second squared, Mr P, Yup.

We get 0 41 meters per second squared 2 sig figs because of the 6 4 seconds Questions Bo, I have 1 Bobby.

Actually I have 1 too, but you can go first Bo Thanks Bobby In the video the velocities weren’t actually negative.

Why not? Mr P, Oh yeah Good eye Bo.

You’re talking about the number shown on the bike right Bo Yup, Mr P.

Well, okay, Billy! What is the name of the item on the bike that is showing the number 23 7 kilometers per hour Billy? I think it’s called a speedometer.

Mr P, Correct. We’re reading that 23 7 kilometers per hour and the 14 3 kilometers per hour off of the speedometer on the bike Notice.

It’s a speedometer, not a velocitometer, A speedometer, not a velocitometer or whatever it would be called displays, just the speed, not the velocity.

So in this particular case it’s giving us the magnitude of the velocity at that particular time.

So the magnitude of velocity at this particular time is going to be the speed and not the velocity.

Now we do know it’s negative, because I’m moving to the left in the video Bo, Okay yeah.

That makes sense Thanks Bobby.

What was your question Bobby My question had, to do with the fact that the bike is.

Speeding up and if the bike is speeding, up shouldn,’t the, acceleration be, positive I, thought that negative accelerations meant that you were slowing down? Mr P, Oh yeah the direction.

I guess we should talk about that.

It is in the title of the video First off realize that we did do the problem correctly. We should end up with a negative acceleration, even though we’re speeding up.

Let,’s talk through why that.

Is by, way of some examples Billy Okay Bobby Good Let’s do that Mr P, Okay, let’s.

Say by way of an example, that I, 39, m riding, my.

Bike, to the right and speeding.

Up In this particular case, that would mean that my velocity would be to the right, and my acceleration would also be to the right and both would be positive because they would be to the right If instead, I’m riding my bike to the right and Slowing down my velocity again is going to be to the right and positive.

However, my acceleration is going to be to the left and negative Billy.

Oh, in other words, when you are speeding up, the acceleration is in the same direction as the velocity Bobby And when you’re slowing down, then the velocity and acceleration are in opposite directions.

Mr P, Exactly If the object is speeding up, that means that the velocity and acceleration are both going to be in the same direction.

However, if the object is slowing down, that means that the velocity and acceleration are going to be in opposite directions, which means, if I am riding my bike to the left and speeding up then, because I’m riding my bike to the left. The velocity is going to be to the left and negative.

If I’m speeding up, then my acceleration is going to be in the same direction as the velocity, which is going to be to the left and negative.

If, however, I am riding my bike to the left and slowing down, that means that my velocity is still going to be to the left and negative.

However, because I’m slowing down, the acceleration is going to be opposite of the direction of the velocity And therefore the acceleration is going to be to the right and positive Bobby Thanks, Mr P.

Now I do think that that bears repeating and writing down on the board Again, if the object is speeding up, the velocity and acceleration are in the same direction and if the object is slowing down the velocity and acceleration are in opposite directions.

Let’s take 1 more look at the 4 examples because darn it.

It took me a long time to film.

Well any more questions Bobby Nope Billy, No Bobby Thanks! Mr P.

Actually, I’m a bit surprised that there aren’t any more questions, because if you look at our acceleration, this is our answer for acceleration.

However, it doesn’t have a direction and acceleration has both magnitude and direction. Unfortunately, because of the problem statement, we didn’t know enough to be able to figure out a direction from the problem.

I kind of did this on purpose because you’re going to run into problems where you’re not given a direction and, alas, you can’t actually figure out a direction in your answer, and this is what you’re going to need to Do So I thought it would be good to go through an example like that, although in the problem they probably should have said something about direction so that you could figure out the direction for your answer, because again, acceleration has both magnitude and direction There you go.

Ladies and gentlepeople, I enjoyed learning with you today.

I hope you enjoyed learning with me.

Voiceover Lecture notes are available at FlippingPhysics com.

Please enjoy lecture notes responsibly, Voiceover You can both film.

At the same time, Child Yeah, Mr P, Hold this Child.

I don’t know how to work this one.

Mr P, It’s the same one, So move forward and stand about here, and I want you to film what mommy and I are going to do Child.

So do you hold it like this? Mr P? Yup, well, you can see what you’re filming Child. Well, I can’t get the whole car.

When do I press record, It is recording right now I’m filming you Child.

No, you’re not supposed to be Child.

I’m, not filming.

I don’t know how Child I got some video.

When do I press record, Mr P, So what I’ll do is I’ll yell 3.

2.

1 brake.

I’ll go over to the other side, So we’re going to do the same thing.

Only I’m going to be on this side of you now Why don’t we head back, I’m going to take some wearing the chest. Harness .

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