Mittlere Geschwindigkeit
About points...
We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
About difficulty...
We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
Question
Solution
Short
Video
\(\LaTeX\)
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Exercise:
Ein Autofahrer legt die Entfernung von mathcalA-Stadt nach mathcalB-Stadt die saO beträgt mit einer mittleren Geschwindigkeit von vaO zurück. Auf der sbO langen Strecke von mathcalB-Stadt nach mathcalC-Stadt ist er etwas schneller und erreicht eine mittlere Geschwindigkeit von vbO. Wie gross ist seine mittlere Reisegeschwindigkeit für die gesamte Strecke von mathcalA-Stadt nach mathcalC-Stadt?
Solution:
Geg s_ saO sa v_ vaO va s_ sbO sb v_ vbO vb GesGeschwindigkeitvsimeterpersecond Der Autofahrer braucht für das erste Teilstück eine Zeitdauer von t_ fracs_ v_ fracsava ta und für das zweite eine Zeitdauer von t_ fracs_ v_ fracsbvb tb. Total hat der Autofahrer also s s_ + s_ sa + sb s währ t t_ + t_ ta + tb t zurückgelegt was Seine mittlere Geschwindigkeit ist daher: v fracst fracs_+ s_t_+ t_ fracs_+s_fracs_v_+fracs_v_ fracs_+s_fracs_v_+s_v_v_v_ fracv_ v_s_+s_v_ s_ + v_ s_ fracst v approx vS vP mittlerer Geschwindigkeit entspricht. v fracv_ v_ s_+ s_ v_ s_ + v_ s_ vS vP
Ein Autofahrer legt die Entfernung von mathcalA-Stadt nach mathcalB-Stadt die saO beträgt mit einer mittleren Geschwindigkeit von vaO zurück. Auf der sbO langen Strecke von mathcalB-Stadt nach mathcalC-Stadt ist er etwas schneller und erreicht eine mittlere Geschwindigkeit von vbO. Wie gross ist seine mittlere Reisegeschwindigkeit für die gesamte Strecke von mathcalA-Stadt nach mathcalC-Stadt?
Solution:
Geg s_ saO sa v_ vaO va s_ sbO sb v_ vbO vb GesGeschwindigkeitvsimeterpersecond Der Autofahrer braucht für das erste Teilstück eine Zeitdauer von t_ fracs_ v_ fracsava ta und für das zweite eine Zeitdauer von t_ fracs_ v_ fracsbvb tb. Total hat der Autofahrer also s s_ + s_ sa + sb s währ t t_ + t_ ta + tb t zurückgelegt was Seine mittlere Geschwindigkeit ist daher: v fracst fracs_+ s_t_+ t_ fracs_+s_fracs_v_+fracs_v_ fracs_+s_fracs_v_+s_v_v_v_ fracv_ v_s_+s_v_ s_ + v_ s_ fracst v approx vS vP mittlerer Geschwindigkeit entspricht. v fracv_ v_ s_+ s_ v_ s_ + v_ s_ vS vP
Meta Information
Exercise:
Ein Autofahrer legt die Entfernung von mathcalA-Stadt nach mathcalB-Stadt die saO beträgt mit einer mittleren Geschwindigkeit von vaO zurück. Auf der sbO langen Strecke von mathcalB-Stadt nach mathcalC-Stadt ist er etwas schneller und erreicht eine mittlere Geschwindigkeit von vbO. Wie gross ist seine mittlere Reisegeschwindigkeit für die gesamte Strecke von mathcalA-Stadt nach mathcalC-Stadt?
Solution:
Geg s_ saO sa v_ vaO va s_ sbO sb v_ vbO vb GesGeschwindigkeitvsimeterpersecond Der Autofahrer braucht für das erste Teilstück eine Zeitdauer von t_ fracs_ v_ fracsava ta und für das zweite eine Zeitdauer von t_ fracs_ v_ fracsbvb tb. Total hat der Autofahrer also s s_ + s_ sa + sb s währ t t_ + t_ ta + tb t zurückgelegt was Seine mittlere Geschwindigkeit ist daher: v fracst fracs_+ s_t_+ t_ fracs_+s_fracs_v_+fracs_v_ fracs_+s_fracs_v_+s_v_v_v_ fracv_ v_s_+s_v_ s_ + v_ s_ fracst v approx vS vP mittlerer Geschwindigkeit entspricht. v fracv_ v_ s_+ s_ v_ s_ + v_ s_ vS vP
Ein Autofahrer legt die Entfernung von mathcalA-Stadt nach mathcalB-Stadt die saO beträgt mit einer mittleren Geschwindigkeit von vaO zurück. Auf der sbO langen Strecke von mathcalB-Stadt nach mathcalC-Stadt ist er etwas schneller und erreicht eine mittlere Geschwindigkeit von vbO. Wie gross ist seine mittlere Reisegeschwindigkeit für die gesamte Strecke von mathcalA-Stadt nach mathcalC-Stadt?
Solution:
Geg s_ saO sa v_ vaO va s_ sbO sb v_ vbO vb GesGeschwindigkeitvsimeterpersecond Der Autofahrer braucht für das erste Teilstück eine Zeitdauer von t_ fracs_ v_ fracsava ta und für das zweite eine Zeitdauer von t_ fracs_ v_ fracsbvb tb. Total hat der Autofahrer also s s_ + s_ sa + sb s währ t t_ + t_ ta + tb t zurückgelegt was Seine mittlere Geschwindigkeit ist daher: v fracst fracs_+ s_t_+ t_ fracs_+s_fracs_v_+fracs_v_ fracs_+s_fracs_v_+s_v_v_v_ fracv_ v_s_+s_v_ s_ + v_ s_ fracst v approx vS vP mittlerer Geschwindigkeit entspricht. v fracv_ v_ s_+ s_ v_ s_ + v_ s_ vS vP
Contained in these collections:
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Geschwindigkeit 1 by uz
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Mehrere Teilstrecken by TeXercises
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Geschwindigkeit I by pw
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Geschwindigkeit 1 by aej
Asked Quantity:
Geschwindigkeit \(v\)
in
Meter pro Sekunde \(\rm \frac{m}{s}\)
Physical Quantity
Geschwindigkeit \(v\)
Strecke pro Zeit
Veränderung des Ortes
Unit
Meter pro Sekunde (\(\rm \frac{m}{s}\))
Base?
SI?
Metric?
Coherent?
Imperial?