Math Problem Statement
En sten faller fritt 45 m. Hur lång tid tar fallet om begynnelsehastigheten är 1,5 m/s?
Solution
För att lösa detta problem kan vi använda den kinematiska formeln för rörelse med konstant acceleration:
där:
- är den totala sträckan (45 m),
- är begynnelsehastigheten (1,5 m/s),
- är accelerationen (här är det tyngdaccelerationen ),
- är tiden som vi vill räkna ut.
Sätt in värdena:
Nu kan vi lösa denna ekvation för . Låt mig beräkna detta åt dig.
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Here are 5 related questions to explore further:
- What happens if the initial velocity is zero instead of 1.5 m/s?
- How does air resistance affect the fall of an object?
- How can we calculate the velocity at the point of impact with the ground?
- What would be the time of fall for different heights (e.g., 60 meters)?
- 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).
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Math Problem Analysis
Mathematical Concepts
Kinematics
Free Fall
Quadratic Equations
Formulas
s = v_0 t + (1/2) a t^2
Quadratic equation: ax^2 + bx + c = 0
Theorems
Quadratic Formula
Suitable Grade Level
Grades 10-12
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