Grafi gibanja so tvoj najbolj zanesljiv prijatelj pri razumevanju fizike!... Show more
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Updated Apr 6, 2026
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Uvod v Grafi Gibanja: Risanje in Razumevanje
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Uvod v grafe gibanja
Zakaj se sploh ukvarjamo z grafi? Ker ti omogočajo, da v trenutku vidiš celotno zgodbo gibanja telesa!
Vedno si zapomni tri ključne tipe: graf poti , graf hitrosti in graf pospeška . Čas je vedno na vodoravni osi, medtem ko je na navpični osi tista količina, ki jo merimo.
Naklon grafa ti pove, kako hitro se kaj spreminja - v s-t grafu predstavlja hitrost, v v-t grafu pa pospešek. Ploščina pod grafom je prav tako pomembna: v v-t grafu predstavlja opravljeno pot, v a-t grafu pa spremembo hitrosti.
💡 Nasvet: Vedno najprej preveri, kaj je na oseh - od tega je odvisno, kako boš interpretiral graf!
Graf poti v odvisnosti od časa
Ta graf ti pove, kje se telo nahaja v določenem trenutku - ne kako hitro se giblje!
Če je graf vodoravna črta, telo miruje (njegova lega se ne spreminja). Če je poševna premica, se telo giblje s konstantno hitrostjo - večji kot je naklon, večja je hitrost.
Pozitiven naklon pomeni gibanje v pozitivno smer, negativen naklon pa gibanje nazaj proti izhodišču. Ko se hitrost spreminja, dobiš krivuljo (parabolo).
⚡ Ključno: Poševna premica na s-t grafu = konstantna hitrost, ne konstanten pospešek!
Graf hitrosti v odvisnosti od časa
To je najpomembnejši graf, ki se pogosto pojavlja na testih! Prikazuje hitrost telesa v vsakem trenutku.
Vodoravna črta na v = 0 pomeni mirovanje. Vodoravna črta nad osjo označuje enakomerno gibanje s konstantno hitrostjo. Poševna premica kaže na enakomerno pospešeno gibanje - naklon je enak pospešku.
Pozitiven naklon pomeni pospeševanje, negativen pa zaviranje. Ploščina pod grafom ti vedno da opravljeno pot - pri pravokotnikih računaš s × v × t, pri trikotnikih pa (osnovna × višina) / 2.
🎯 Za teste: Naklon v v-t grafu = pospešek, ploščina = pot!
Graf pospeška in praktični primer
Graf pospeška je najlažji za razumevanje. Vodoravna črta na a = 0 pomeni mirovanje ali enakomerno gibanje, medtem ko konstantna vrednost nad ali pod osjo predstavlja enakomerno pospešeno gibanje.
Poglejmo praktični primer: avto spelje, vozi s konstantno hitrostjo, nato zavira. Na v-t grafu vidiš tri dele - pospeševanje (naraščajoča premica), enakomerno gibanje (vodoravna premica) in zaviranje (padajoča premica).
Pri računanju pospeška uporabiš formulo a = Δv/Δt. Skupno pot dobiš tako, da sešteješ ploščine vseh oblik pod grafom.
📝 Opomnik: Pri zaviranju je pospešek negativen - to ni napaka, ampak fizikalno dejstvo!
Reševanje nalog korak za korakom
Ko rešuješ naloge, vedno sledi istemu postopku. Najprej opiši gibanje v posameznih intervalih, nato izračunaj pospešek preko naklona in nazadnje določi pot preko ploščine.
Za pospešek uporabiš naklon: a = /. Za pot sešteješ ploščine - pravokotnik je dolžina × širina, trikotnik pa (osnovna × višina)/2.
V našem primeru z avtomobilom: pospeševanje traja 4 s z a = 2,5 m/s², enakomerno gibanje 6 s, zaviranje pa 2 s z a = -5 m/s². Skupna pot je 90 m.
🔥 Trick: Naredi si skico in označi vse vrednosti - tako se ne boš zmotil pri računanju!
Najpogostejše napake in hitra tabela
Pozor na napake! Ne zamenjuj grafov - poševna premica na s-t grafu pomeni konstantno hitrost, na v-t grafu pa konstanten pospešek. Vedno preveri enote na oseh!
Negativne vrednosti niso napaka: hitrost je lahko negativna (gibanje v nasprotno smer), pospešek pa je negativen pri zaviranju. Pot je običajno pozitivna.
| Graf | Naklon | Ploščina |
|---|---|---|
| s-t | Hitrost (v) | / |
| v-t | Pospešek (a) | Pot (s) |
| a-t | / | Sprememba hitrosti (Δv) |
🏆 Za odličen test: Znaš razpoznati oblike grafov in veš, kaj predstavljajo naklon ter ploščina!
Hitri povzetek oblik grafov
Mirovanje: s-t je vodoravna premica, v-t je črta na v = 0, a-t je črta na a = 0.
Enakomerno gibanje: s-t je poševna premica, v-t je vodoravna premica , a-t ostane na a = 0.
Enakomerno pospešeno gibanje: s-t je parabola, v-t je poševna premica, a-t je vodoravna premica .
✨ Končni nasvet: Naredi si lastne skice za vsako vrsto gibanja - vizualni spomin je najmočnejši!
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Most popular content in Fizika
Most popular content
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5
App Store
4.7/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
Uvod v Grafi Gibanja: Risanje in Razumevanje
Grafi gibanja so tvoj najbolj zanesljiv prijatelj pri razumevanju fizike! Namesto da se ukvarjaš s kompleksnimi formulami, ti grafični prikazi na hiter pogled pokažejo, kako se telo giblje - ali miruje, se premika s konstantno hitrostjo ali pospešuje.
Uvod v grafe gibanja
Zakaj se sploh ukvarjamo z grafi? Ker ti omogočajo, da v trenutku vidiš celotno zgodbo gibanja telesa!
Vedno si zapomni tri ključne tipe: graf poti , graf hitrosti in graf pospeška . Čas je vedno na vodoravni osi, medtem ko je na navpični osi tista količina, ki jo merimo.
Naklon grafa ti pove, kako hitro se kaj spreminja - v s-t grafu predstavlja hitrost, v v-t grafu pa pospešek. Ploščina pod grafom je prav tako pomembna: v v-t grafu predstavlja opravljeno pot, v a-t grafu pa spremembo hitrosti.
💡 Nasvet: Vedno najprej preveri, kaj je na oseh - od tega je odvisno, kako boš interpretiral graf!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Graf poti v odvisnosti od časa
Ta graf ti pove, kje se telo nahaja v določenem trenutku - ne kako hitro se giblje!
Če je graf vodoravna črta, telo miruje (njegova lega se ne spreminja). Če je poševna premica, se telo giblje s konstantno hitrostjo - večji kot je naklon, večja je hitrost.
Pozitiven naklon pomeni gibanje v pozitivno smer, negativen naklon pa gibanje nazaj proti izhodišču. Ko se hitrost spreminja, dobiš krivuljo (parabolo).
⚡ Ključno: Poševna premica na s-t grafu = konstantna hitrost, ne konstanten pospešek!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Graf hitrosti v odvisnosti od časa
To je najpomembnejši graf, ki se pogosto pojavlja na testih! Prikazuje hitrost telesa v vsakem trenutku.
Vodoravna črta na v = 0 pomeni mirovanje. Vodoravna črta nad osjo označuje enakomerno gibanje s konstantno hitrostjo. Poševna premica kaže na enakomerno pospešeno gibanje - naklon je enak pospešku.
Pozitiven naklon pomeni pospeševanje, negativen pa zaviranje. Ploščina pod grafom ti vedno da opravljeno pot - pri pravokotnikih računaš s × v × t, pri trikotnikih pa (osnovna × višina) / 2.
🎯 Za teste: Naklon v v-t grafu = pospešek, ploščina = pot!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Graf pospeška in praktični primer
Graf pospeška je najlažji za razumevanje. Vodoravna črta na a = 0 pomeni mirovanje ali enakomerno gibanje, medtem ko konstantna vrednost nad ali pod osjo predstavlja enakomerno pospešeno gibanje.
Poglejmo praktični primer: avto spelje, vozi s konstantno hitrostjo, nato zavira. Na v-t grafu vidiš tri dele - pospeševanje (naraščajoča premica), enakomerno gibanje (vodoravna premica) in zaviranje (padajoča premica).
Pri računanju pospeška uporabiš formulo a = Δv/Δt. Skupno pot dobiš tako, da sešteješ ploščine vseh oblik pod grafom.
📝 Opomnik: Pri zaviranju je pospešek negativen - to ni napaka, ampak fizikalno dejstvo!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Reševanje nalog korak za korakom
Ko rešuješ naloge, vedno sledi istemu postopku. Najprej opiši gibanje v posameznih intervalih, nato izračunaj pospešek preko naklona in nazadnje določi pot preko ploščine.
Za pospešek uporabiš naklon: a = /. Za pot sešteješ ploščine - pravokotnik je dolžina × širina, trikotnik pa (osnovna × višina)/2.
V našem primeru z avtomobilom: pospeševanje traja 4 s z a = 2,5 m/s², enakomerno gibanje 6 s, zaviranje pa 2 s z a = -5 m/s². Skupna pot je 90 m.
🔥 Trick: Naredi si skico in označi vse vrednosti - tako se ne boš zmotil pri računanju!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Najpogostejše napake in hitra tabela
Pozor na napake! Ne zamenjuj grafov - poševna premica na s-t grafu pomeni konstantno hitrost, na v-t grafu pa konstanten pospešek. Vedno preveri enote na oseh!
Negativne vrednosti niso napaka: hitrost je lahko negativna (gibanje v nasprotno smer), pospešek pa je negativen pri zaviranju. Pot je običajno pozitivna.
| Graf | Naklon | Ploščina |
|---|---|---|
| s-t | Hitrost (v) | / |
| v-t | Pospešek (a) | Pot (s) |
| a-t | / | Sprememba hitrosti (Δv) |
🏆 Za odličen test: Znaš razpoznati oblike grafov in veš, kaj predstavljajo naklon ter ploščina!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Hitri povzetek oblik grafov
Mirovanje: s-t je vodoravna premica, v-t je črta na v = 0, a-t je črta na a = 0.
Enakomerno gibanje: s-t je poševna premica, v-t je vodoravna premica , a-t ostane na a = 0.
Enakomerno pospešeno gibanje: s-t je parabola, v-t je poševna premica, a-t je vodoravna premica .
✨ Končni nasvet: Naredi si lastne skice za vsako vrsto gibanja - vizualni spomin je najmočnejši!
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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Most popular content in Fizika
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Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5
App Store
4.7/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user