Finding acceleration value for kinematic equation with t²

[User72564]

Homework Statement

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Homework Equations

The Attempt at a Solution

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Hey, I did part a and b. Although I need a little help with part c.
I know you're supposed to solve for t^2 but I don't know what value to use for acceleration.
I'd use the quadratic formula to solve for t^2, but I'm just not sure which values to use...
At first I thought the initial velocity would be zero and the acceleration would be zero but then that left me with:

-1/2 * (4.8 m/s^2) = 0 which doesn't lead to the right answer. Could you guys point me in the right direction?

 

[User72564]

I ended up just differentiating then doing 0.36T^2 - 4.8T = 0 ---> (0.36T^2) / (0.36T) = (4.8t)/ (0.36T) which gave the right answer, but I wanted to know if there was a way to use the quadratic formula and the above equation since that's how the example in the book was done. I guess at this point its kind of an algebra question than a physics question.

 

[Daymare]

You can't use the one dimensional equation you have given in the first post as in this case the acceleration is not constant.