Trouble with kinematics and other basic physical concepts

[Lord Satin]

[You don't need to read the whole thing, but I'd recommend doing so, because there are examples of my struggles somewhere in there, like specific problems.]

Greetings as usual,

It's me again. That hopeful physicist who somehow found himself at the wrong place with the wrong mind in the wrong situation. So I've got a pretty severe issue right now...

School's finished. I'll be seeing my high school for the first time in two months! Tenth year by the way, not ninth. Different system. High school is year 10-14 (or 10-12, if you get a skill). So, since I was in a special needs school (don't ask how I got there, it's quite embarrassing), which impeded my progress quite severely, I taught myself a lot of stuff like trig or precalc to compensate. But I completely forgot about my lacking knowledge of physics!

So now I'm revising with Khan Academy. Trying to make up for all those lost opportunities for a proper education. Maths are going alright. Could be worse. But my physics knowledge is atrocious! Our teacher apparently forgot to teach us anything but the basic concepts! Now that I think back, we never did actual problems on physics, so I think that could be it.

Basically, I can't solve any problems at all. I could solve a problem with a constantly decelerating spaceship perfectly and within seconds. But when it comes to cars, people, koalas, flying chickens or hamsters moving across graphs? No way. I'm hitting a wall.

I really don't know why, but I can't seem to get a basic grasp of kinematics. I'm seriously struggling. There's a question about a book falling from a window that's 13.7 meters high. It asks how fast (I mean, in how much time) the book falls to the ground, without any air resistance. Acceleration is constant, 9.82m/s^2. So I applied logic (I wanted to see if I could finish it without the tutorial), and said that in the first second, it travels 9.82 meters down. In the second second (odd word connection), it traveled twice as far (since it accelerated). So I took 13.7 and subtracted the 9.82 meters that the book already traveled. Then I found that after those 9.82 meters, the book has a velocity of 19,64 m/s. So I used that classic formula I still miraculously remember; t = d/v. So I take 3.88 and divide it by 19.64. I get a result, add it to the one second I recorded from before, and behold... It's wrong. Almost half a second off.

So there. I don't get it. Am I going too far ahead? We were taught Newtonian physics in 6th grade (the concepts anyway), but maybe it's revised and done more in-detail later? I see lots of 10th years talking about kinematics, so I'm a bit confused.

Even if that's true, I don't know why I have so much trouble understanding such a simple concept. I don't rely on formulas. I don't like doing it. If I can't figure it out, I'll look, but I usually get too angry to remember them!

It's a real shame, because I want to understand. I want to walk outside, look at a tram, and understand what makes it move. I want to be able to look at the world around me and realize that I understand what makes it tick. I want to face challenging problems that require solutions. But it looks like I might not be quite good enough after all.

It'd be a real shame if my dream came crashing down just because of motion physics...

Anyone know any way to fix this issue? Any experiences? Advice? I'm desperate for help, because not even Khan Academy can help me now. And we all know that when Khan Academy can't help, the situation is truly dire...

Thanks!

 

[axmls]

Kinematics and the relationship between acceleration, velocity, and position are not possible to adequately learn until you've learned calculus. Don't worry about it.

 

[Lord Satin]

Oh thank goodness... I was afraid that my school didn't teach me necessary knowledge. I'm generally confused about the levels of material in physics/mathematics. It's different here than in the US and UK, so I thought I was missing something I needed.

Thanks for the reply. Now I can rest easy...

 

[Lord Satin]

Yeah... That went through my mind as well. Obviously objects don't just switch to another gear mid-flight. The change is gradual. But here's the problem. How am I supposed to measure it properly when you can just split every interval of time in half? Doesn't matter how small the interval is, there's always a smaller one, and the velocity is always slightly different. So to absolutely 100% correctly measure the dynamic velocity of any object in motion, I need to do an infinite amount of equations? After all, to properly do it, I suppose I'd have to measure the object's velocity at every moment in time. But there can be infinite moments in time, just as there can be an infinite number of differing velocities...?

Never seen that formula, unfortunately. I suppose calculus helps a lot though. Heard calculus deals with these tiny fragments of whatever you're measuring to make a good estimate.

Thanks for the reply! Appreciate it! I'll use that formula from now on. But it is just a really precise estimate overall, right? Or does it actually measure the exact time it takes for an accelerating object to move across a distance?

 

[jtbell]

Oops, I see you managed to respond to my original post before I deleted it after realizing I needed to rewrite it. You're fast.

There's a question about a book falling from a window that's 13.7 meters high. It asks how fast (I mean, in how much time) the book falls to the ground, without any air resistance. Acceleration is constant, 9.82m/s^2. So I applied logic (I wanted to see if I could finish it without the tutorial), and said that in the first second, it travels 9.82 meters down.

No, at the end of the first second, it has a velocity of 9.82 m/s. An acceleration of 9.82 m/s² means that the velocity changes at the rate of 9.82 m/s per second.

This does not mean that it has traveled 9.82 m during that second, as the "classic formula" v = d/t or d = vt would seem to indicate. That formula works only for constant velocity, and the velocity is not constant in this case... it increases steadily during that second. from 0 m/s to 9.82 m/s!

You run into the same error later on:

Then I found that after those 9.82 meters, the book has a velocity of 19,64 m/s. So I used that classic formula I still miraculously remember; t = d/v. So I take 3.88 and divide it by 19.64.

Your book probably introduces another "classic formula", $d = \frac 1 2 a t^2$, for the distance traveled by an object during time t with constant acceleration a, starting from rest. This gives the correct answer for this problem.

 

[Lord Satin]

I see. So the object didn't travel 9.82 meters in the first second? Right. Of course. That makes sense. That would be if it had a velocity of 9.82m/s. I don't know why I didn't realize that when I was solving the problem... But it's like I said, it wouldn't help me at all. Since I don't really have any good books yet, I'd be stuck trying to find the infinite miniature increases in velocity every femtosecond (or less) to find out how far the object traveled. Suppose I'd have to be a supercomputer to solve it that way. And even that might not suffice.

I was trying to solve it by logic and from experience. Thinking I had already covered this in the past somewhere. I was wrong. This is something new and I am indeed ahead of time.

That formula will make it a lot easier for me. Thank you.

Edit: Aye. I'm constantly on edge, waiting for replies on any site with notifications! Never go outside, so I'm stuck, brain rotting while I spend the summer in boredom. Talking to people on the Internet is a nice change of pace. At least it isn't solitude.

 

[Lord Satin]

Oh... I just had a look at that thing with the (countably) infinitely small fragments of time... Apparently someone already came up with it before me. Super Tasks or something. I thought I had been the first. How naive of me. It seems that everything has been figured out already!

What a shame!

 

[axmls]

Since I don't really have any good books yet, I'd be stuck trying to find the infinite miniature increases in velocity every femtosecond (or less) to find out how far the object traveled

What you're describing is calculus.

 

[micromass]

Why don't you teach yourself some basic calculus if you don't like to rely on formulas?

 

[Lord Satin]

Easier said than done. Calculus seems very complex, from what I can see. In any case, I looked at a few videos some time before, and yes. I can see now that calculus would be extremely useful for physics. It's obvious now that without calculus, I can't really solve many physics problems at all, at least not from kinematics (though I did solve a few that involved constant acceleration and time that wasn't a fraction).

Right now, I'm trying to teach myself. Been doing it since Friday, I believe. Since I took a break on the weekend, I'm still on limits. But I'll keep on trying! I'll keep on pressing whatever I can into my damaged brain, get it as dense as possible! Just hope I won't overheat it in the process.

Thank you all for the advice! And most of all, thank you for showing me the importance of calculus!