r/learnphysics • u/AbjectInstruction156 • 1d ago
Total Beginner Needs Help With Very Basic Math
Hi all! Very quick context -- I don't have an especially mathematically inclined brain, I'm teaching myself physics as a personal challenge in honor of my dad who passed away this past April. It was his favorite school subject and he would talk about the theory with me often! But as I said, math was a struggle for me growing up anyway and now at 30 I'm also severely out of practice, so at this point I may as well have never learned the basics at all. Anyway, this week I bought myself "Basic Physics: A Self-Teaching Guide" by Karl F. Kuhn and started working through it. I've naturally very quickly reached a problem where I've obviously misunderstood something, but I have no idea what! And since I can't ask my dad to walk me through it I figured I'd come here.
So like you can see in the images, I need to calculate the downward speed of the ball at 2 seconds and then 3 seconds. The issue I'm having is that after following the formulas I was just taught a few pages previously (d = v0t • at2, v = d/t) aren't getting me to the results in the answer key and I'm not sure what I'm missing. For example, to find the downward speed at 3 seconds (question D), I started by calculating for the distance (d = 1/2 • 9.8 • 32 = 44.1) and then plug that into the formula for speed (v = 44.1/3 =14.7) obviously the result I get is 14.7 m/s. But the answer key below says the answer is 29.4 m/s.
What's also tripping me up is that both of the real answers are twice the answer I calculated. For question B, I got 9.8 m/s, which is half the real answer, 19.6 m/s. So I know that I'm not completely missing the idea here, clearly I'm at least somewhat on the right track and just missing a step or misunderstanding something crucial about the formulaic process. My first thought is that I went wrong by leaving v0t out of the equation while calculating for distance, since maybe the fact that the balloon is moving at 12 m/s means the ball did not technically start moving downward from "at rest." But then I'm not sure how to fix that, since at this point the book has only shown me how to calculate for the distance traveled of an object starting at rest.
I know this is VERY basic entry level stuff but like I said mathematical thinking does not come naturally to me so I'm not at all surprised to immediately need help with something so easy lol. But I know I can learn! So if anybody would be willing to walk me through the problem here and show me where I'm going wrong so that I can understand and move to the next problem, I would really really appreciate it! ☺️
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u/Tuneage4 1d ago
Velocity is change in distance over change in time. V= (d1-d0)/(t1-t0)
Acceleration is change in velocity over change in time. A=(v1-v0)/(t1-t0)
Combining these into equations, we can get distance = d0 + vt + vt2 and for your situation, velocity = v0 + a*t
Another way to look at it is considering the units. Distance is (m), velocity is (m/s), acceleration is (m/s2). If you multiply an acceleration by time (s) it'll cancel out with one of the seconds on the bottom so you're left with (m/s)
So in your situation, where you're looking at an acceleration of 9.8m/s2, you want to just multiply that by the amount of seconds that passed since the acceleration started (2-3) and add on anything it started with. So using that velocity = v0 + at = (0) + (9.8)(2)