# What do you mean by average speed

## Big Bang HTL 3, textbook

6 Selected Chapters of Classical Physics (3rd year, 5th semester) 1.2 Flight to the stars Differentiating and integrating This section deals with one of the most important mathematical achievements of modern times, namely differential and integral calculus. The higher physics is inconceivable without these mathematical tools! Should you ever forget the definition of speed, then think of the speedometer. This shows kilometers per hour. The speed is thus defined as distance per time and specified in the SI system with m / s (F7). What do you mean by average and current speed? Radar measurements and section control are available to prevent the lawn in traffic. In both cases the speed is measured. But there is a huge difference! Which one is it? What is meant by “deriving” in mathematics? What does the derived function represent? How are speed and acceleration defined? What is the slope of the straight line in an s - t diagram and in a v - t diagram (see Fig. 1.7 and 1.8). Sometimes you read that sprinters can run the 200m at a higher speed than the 100m. Can it really be? Help you with Fig. 1.6. How is it related to question 4? It is logical that a straight line has a slope. But does a curve also have an incline? For example, is it possible to specify the slope of the v - t curves in Fig. 1.6? The gravitational acceleration g has the strange unit m / s 2. Where does the square in the denominator come from? F4 A1 F5 A2 F6 A1 F7 A1 F8 A2 Fig. 1.6: Speed ​​curves in the men's 100m and 200m run: This is a v - s diagram! F9 A2 F10 A1 Formula: speed v = ∆ s __ ∆ t ⇒ ∆ s = v · ∆ tv… speed [v] = m / s ∆ s… distance [∆ s] = m ∆ t… time interval [∆ t] = s But what is the speed of this definition? To get the average speed (F4)! If you drive from Vienna to Salzburg (about 300 km) and it takes you 3 hours, the average speed is 100 km / h. However, this value does not tell you how you drove. You can drive steadily or speed and take a longer coffee break in between. Of course, you can't tell from the number. The average speed is also measured with Section Control (F5). This determines how much time elapses between two measuring points and calculates from this. During a radar control, however, the Doppler effect (see chapter 3.3, p. 29) measures how fast you are driving at that moment. A physicist would say that the instantaneous speed is measured (F4). Who runs faster: a 100m or a 200m runner (F8)? That depends on what speed you mean! If you only have the time for the entire distance, then you can only calculate the average speeds (similar to Section Control). For that matter, usually the 200m runners are actually faster. As far as the maximum speed is concerned, i.e. the current speed in the fastest section, the 100m runners have the edge (see Fig. 1.6). This is due to the fact that the start, in particular, depresses the average speed - you start at zero speed. 200m sprinters start the second half at full speed, saving almost a second. On earth, an object in free fall has a speed of around 10m / s after one second, 20m / s after 2 seconds and so on. The speed increases by 10m / s per second. 10m / s per second is 10 (m / s) / s or 10m / s 2. Therefore one says that the earth's acceleration (g) is 10m / s 2 (F10). On the moon, the gravitation is only 1/6 of that on earth. Therefore the lunar acceleration is only 1.67m / s 2. In general, acceleration is defined as the change in speed over time (F7). Formula: Acceleration a = ∆ v __ ∆ t ⇒ ∆ v = a · ∆ ta… acceleration [a] = [v] / [t] = (m / s) / s = m / s 2 ∆ v… change in speed [∆ v] = m / s ∆ t… time interval [∆ t] = s FF For testing purposes only - property of the publisher öbv