Verifying: Solving Quadratic Equations for Time

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SUMMARY

The discussion focuses on solving quadratic equations to determine the time an object reaches a specific height during its motion. The equation used is x = x0 + v0t + (1/2)at², which is quadratic in nature, leading to two possible solutions for time t. This duality arises because the object passes through the initial height twice: once while ascending and once while descending. Understanding this concept is crucial for accurately interpreting the physical implications of the quadratic formula in motion scenarios.

PREREQUISITES
  • Understanding of kinematic equations, specifically x = x0 + v0t + (1/2)at²
  • Basic knowledge of quadratic equations and their properties
  • Familiarity with the concepts of initial velocity and displacement
  • Concept of projectile motion and its characteristics
NEXT STEPS
  • Study the derivation and applications of the quadratic formula in physics
  • Explore kinematic equations in-depth, focusing on their graphical representations
  • Learn about projectile motion and the factors affecting its trajectory
  • Investigate real-world examples of objects in motion to apply these concepts
USEFUL FOR

Students studying physics, particularly those focusing on kinematics, educators teaching motion concepts, and anyone interested in the mathematical modeling of physical phenomena.

savva
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Could anyone please verify with me that I have the right idea in answering the question below.

Homework Statement


If you know the initial velocity v0 and the initial and final heights y0 and y, you can use x=x0+v0t+(1/2)at^2 to solve for the time t when the object will be at height y. But the equation is quadratic in t, so you'll get two answers. Physically, why is this?

The Attempt at a Solution


This occurs because during the motion of an object it has passed through it's initial displacement on 2 occassions. Thus times occur twice.
 
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One on the way up and the other on the way down probably.
 

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