Homework Interlude 1: Please Excuse My Dear Aunt Sally

I had a big problem with my homework, but I figured it out.

Oh? What was it?

I knew I had to use those equations you gave me to fill out the tables, but it turned out I was reading them wrong.

How so?

Well, you wrote , so I took the velocity 0.3 and the position 0 and I added them to get 0.3, then multiplied by 0.1, giving me , which is my new position. Then I did it again, 0.3+0.3 times 0.1 is 0.06. And then I get 0.036, and then 0.0096, and that started to look crazy, because the position is getting smaller each time.

Yeah, it does look crazy. What did you figure out?

I asked your dad and he reminded me of PEMDAS, Please Excuse My Dear Aunt Sally.

And what is that?

It’s the order of operations. Parentheses, Exponentiation, Multiplication, Division, Addition, Subtraction. So when you wrote it means to multiply first, then add . I was doing things in the wrong order, and that’s why my answers came out crazy.

That’s right, and I guess it’s my fault for not explaining that! I’m glad you figured it out.

It’s alright. What’s funny is that once he said “Please Excuse My Dear Aunt Sally” a vague memory of it came back. I remembered the phrase but had always assumed it was a line from some forgotten song from my childhood.

Ha ha. I guess since you figured that out we can review the homework. You were supposed to repeat the exercise that we did last week and generate your own tables of position and velocity using whatever rule you wanted for acceleration. And then you were supposed to plot some position versus time graphs. Let’s see what you’ve got.

Mom's table of values for a constant acceleration

Tell me how you generated the values in this table here.

Okay, I started with this position and this velocity at the top. Then I used the formula you gave me. So I take the velocity and I multiplied it by 0.1, then I add that to the position, and that gives me the new position, 0.6. Then I used , and I multiply that by 0.1, and add it to the velocity, which gives me the new velocity, 3.5. And then I repeated that. Is that right?

It’s exactly right. Good job. Now can we look at the plots? You have two, it looks like; one with constant velocity and one with constant acceleration.

 

Mom's plots of time versus position. The one that makes a straight line has a constant velocity. The others have

 

acceleration

 

The constant velocity one looks good. But the one with constant acceleration is looking strange. Shouldn’t the accelerating curve cross the constant velocity curve because it’s going faster and will have a bigger position? See, in your table here —- Oh wait! I see what happened.

The plots viewed the conventional way, with time on the horizontal axis and position on the vertical axis.

You put time on the horizontal axis, so I was looking at it backwards, but if I flip it around like this, it looks just right. You see how it’s curving up, getting further and further away from the constant velocity one? That’s just what we want. Good job on your homework.

Thank you.

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