Graphical Representation and Problem Solving in Uniformly Accelerated Motion
This page continues the analysis of the stone's motion, focusing on graphical representation and problem-solving techniques for gleichmäßig beschleunigte Bewegung (uniformly accelerated motion).
The page presents a position-time graph (x-t diagram) based on calculations from the previous page. This graph visually represents the stone's motion over time.
Highlight: The position-time graph provides a clear visual representation of the stone's trajectory, showing its rise and fall.
A verbal description of the stone's motion is provided, explaining that it is launched with an initial velocity of 30 m/s, rises with decreasing velocity until it reaches its turning point at 6 seconds, and then falls back down with increasing velocity.
Example: The stone's motion is described as: "The stone is shot from the catapult at 30 m/s and then initially shoots upwards with ever-slowing velocity until the turning point, which it reaches after 6 seconds. From there it falls back down, and the velocity with which it falls becomes ever higher."
The final part of the page focuses on solving the problem of when the stone is 30 m above and below the catapult. This involves using the quadratic equation derived from the motion equation:
x(t) = -5m/s² · t² + 30m/s · t
The solution demonstrates the application of the quadratic formula to find the time values when the stone reaches these specific positions.
Vocabulary: The quadratic formula, also known as the "pq-Formel" in German, is used to solve quadratic equations in the form ax² + bx + c = 0.
This page effectively ties together the theoretical concepts of uniformly accelerated motion with practical problem-solving techniques, emphasizing the importance of both mathematical and graphical approaches in physics.
