Use a(t)= -32 feet per second squared as the acceleration due to gravity. A ball is thrown vertically upward from the ground with an initial velocity of 96 feet per second. How high will the ball go.
The velocity is $\displaystyle v(t)=\int a(t)dt=-32t+C$ where $\displaystyle C$ is the initial velocity. Therefore, the velocity function is:
$\displaystyle v(t)=-32t+96$
So now you have to find the point where $\displaystyle v(t)=0$, since this is the point where the ball is at the maximum hieght. Since the ball started at the ground, the initial position is $\displaystyle C_2=0$, so see if you can find the deduce the maximum height with this information. Just think about the relationship between velocity and position.