I'm pretty sure I'm doing this right. .

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AI Thread Summary
The discussion focuses on solving for the times when a turtle, moving along the x-axis, is 10 cm from its initial position based on the given position equation. The user has already calculated the first two times as 6.2 seconds and 25.8 seconds but is struggling with the third time, mistakenly suggesting 38.2 seconds. Recommendations include graphing the equation to visualize the points where the turtle is at 10 cm and solving the quadratic equations derived from the position function. The user confirms they understand the solution after receiving guidance. The conversation emphasizes the importance of precise calculations and graphical analysis in solving motion problems.
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Homework Statement



A turtle crawls along a straight line, which we will call the x-axis with the positive direction to the right. The equation for the turtle's position as a function of time is
x(t)=50.0 cm+(2.00cm/s)t-(0.0625 cm/s^2)t^2

At what time t will the turtle be 10 cm from his initial position for the 1st, 2nd, and 3rd times

Homework Equations



s(x)= r + v(t) - gt^2

The Attempt at a Solution



I have solved already for the first and second times for 6.2 and 25.8. I also figure that it takes 32 seconds to reach the initial point. My reasoning would be 32+6.2 giving me 38.2, but that seems to be wrong. Any help please.
 
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I don't get the 38.2. Recommend you graph
y = 2t-0.0625*t^2
and see when it is 10 or -10.
Then solve -0.0625*t^2 + 2t -10 = 0
and -0.0625*t^2 + 2t +10 = 0
to get the answers more precisely.
 
Yeah, I got it. Thanks.
 

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