Physical Interpretation for two answers for time

AI Thread Summary
The motion equation x = x_0 + v_0t + (1/2)at^2 yields two solutions for time (t), one of which is negative due to the quadratic nature of the equation. The negative time represents the moment in the past when the object would have been at the initial height (x_0) before being thrown. The positive time indicates when the object will reach the ground after being thrown. This duality in time solutions reflects both past and future events in the object's motion. Understanding this concept clarifies the physical interpretation of the equation's results.
mateomy
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When you solve the motion equation

<br /> x=x_0 +v_0t +\frac{1}{2}at^2<br />

you get two answers for t. One being a negative due to the quadratic. What is the physical interpretation of this? Its driving me nuts.
 
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hi mateomy! :smile:
mateomy said:
you get two answers for t. One being a negative due to the quadratic. What is the physical interpretation of this? Its driving me nuts.

that's the standard constant acceleration equation for a particle going vertically up at speed v0 and height x0 at time t …

the two values of t for x = 0 are the time in the future when it will hit the ground, and the time in the past when it would have left the ground if it had been thrown from there (or below) :wink:
 
Go'bless you, Toiny Tim (Harsh cockney accent). What if, say...it left from the ground?
 
wotcher, me ol' mateomy! :wink:
mateomy said:
Go'bless you, Toiny Tim (Harsh cockney accent). What if, say...it left from the ground?

from the foot of the apples an' pears?

then the negative answer would be the time before it reaches height x0 …

'nuff said? o:)​
 
Got it down solid now. Thanks for the clarification.
 

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