En sten faller fritt 45 m. Hur lång tid tar fallet om begynnelsehastigheten är 1,5 m/s?


För att lösa detta problem kan vi använda den kinematiska formeln för rörelse med konstant acceleration:

\[
s = v_0 t + \frac{1}{2} a t^2
\]

där:
- \( s \) är den totala sträckan (45 m),
- \( v_0 \) är begynnelsehastigheten (1,5 m/s),
- \( a \) är accelerationen (här är det tyngdaccelerationen \( g = 9,8 \, \text{m/s}^2 \)),
- \( t \) är tiden som vi vill räkna ut.

Sätt in värdena:

\[
45 = 1,5t + \frac{1}{2} \times 9,8 \times t^2
\]

Nu kan vi lösa denna ekvation för \( t \). Låt mig beräkna detta åt dig.

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Here are 5 related questions to explore further:
1. What happens if the initial velocity is zero instead of 1.5 m/s?
2. How does air resistance affect the fall of an object?
3. How can we calculate the velocity at the point of impact with the ground?
4. What would be the time of fall for different heights (e.g., 60 meters)?
5. How does the gravitational acceleration vary across different planets?

**Tip:** When solving quadratic equations, there are often two solutions; one is physically meaningful for time (positive value).

En sten faller fritt 45 m. Hur lång tid tar fallet om begynnelsehastigheten är 1,5 m/s?

Learn how to calculate the time it takes for a stone to fall freely from a height of 45 meters with an initial velocity of 1.5 m/s using kinematic equations. This detailed solution includes the use of the quadratic equation formula and is suitable for students in Grades 10-12.

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