A Problem I Was Considering But Seems So Simple

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A ball thrown into the air has equal speeds at the second and third seconds of its flight. The discussion revolves around determining the ball's velocity at time zero, with suggestions that there may be two potential answers, one being negative. The concept of symmetry in projectile motion is emphasized, indicating that the ball's upward and downward speeds are equal at corresponding times. The initial velocity is critical to understanding the ball's motion, and a negative initial velocity would imply a downward throw rather than an upward one. The conversation encourages solving the problem using these principles of symmetry and speed equality.
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A ball is thrown up in the air and the speed of the ball at the second second is equal to the speed of the ball after the third second. But what would be the velocity of the ball when the time equals zero.

I have been thinking about this a lot and I'm certain that there are two answers (and I think one is negative)
 
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Show how you solved it. (A negative initial velocity wouldn't get you very far.)

Hint: Use symmetry.
 
Another hint: The speeds are equal.
 

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