Verifying: Solving Quadratic Equations for Time

AI Thread Summary
The discussion centers on solving quadratic equations to determine the time an object reaches a specific height during its motion. The equation x = x0 + v0t + (1/2)at^2 results in two solutions for time, reflecting the object's ascent and descent through the same height. This duality arises because an object can pass a given height twice: once while moving upward and again while descending. Understanding this concept is crucial for accurately interpreting the physical implications of the quadratic solutions. The explanation highlights the importance of recognizing the two distinct moments in the object's trajectory.
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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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