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:

s=v0t+12at2s = v_0 t + \frac{1}{2} a t^2

där:

  • ss är den totala sträckan (45 m),
  • v0v_0 är begynnelsehastigheten (1,5 m/s),
  • aa är accelerationen (här är det tyngdaccelerationen g=9,8m/s2g = 9,8 \, \text{m/s}^2),
  • tt är tiden som vi vill räkna ut.

Sätt in värdena:

45=1,5t+12×9,8×t245 = 1,5t + \frac{1}{2} \times 9,8 \times t^2

Nu kan vi lösa denna ekvation för tt. 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).

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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