Integration and initial velocity

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Homework Statement

With what initial velocity must an object be thrown upward (from ground level) to reach a maximum height of 550feet.

Use a(t)= -32ft/sec² as the acceleration due to gravity. (neglect air resistance)

Homework Equations

Use integration

The Attempt at a Solution

I know that U should first start off by integrating the acceleration in order to get velocity, but I wind up getting:

32x+C= v(t)

I'm not sure how to deal wit the problem from here, does anyone have any suggestions?

 

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What is x?

 

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Im pretty sure that x is suppose to be time, because that is the only thing that relates acceleration and velocity

 

[CompuChip]

I thought t was time as well. So lesson one is to be a bit more precise in your notation.

a(t) = -32 ft/s², then
$$v(t) = \int a(t) \, dt$$
where t is the variable. Integrating a constant over t gives you the constant times t so
v(t)[ft/s] = - 32 t + C

Note the minus sign, which is carried over from a(t) < 0.
C is an integration constant which you need to determine. What condition will you use for this?
How can you see in the v(t) graph or formula that the highest point is reached?