# Homework Help: Integration and initial velocity

1. Jan 26, 2009

### toasted

1. The problem statement, all variables and given/known data

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)

2. Relevant equations

Use integration

3. 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?

2. Jan 26, 2009

### CompuChip

What is x?

3. Jan 26, 2009

### toasted

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

4. Jan 27, 2009

### 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?