The problem is "A ball is thrown vertically upward from ground level with an initial velocity of 96ft per second. Assume acceleration of -32 ft/sec^2.
1) After how many seconds is the velocity of the ball one-half the initial velocity?
2) What is the height of the ball when the velocity is one-half the initial velocity?
Start by writing an expression for the velocity v(t) as a function of time. You should be able to get the answer to #1 from just that. Then if you integrate the velocity $\displaystyle \int v(t)\,dt$, that should give you the position s(t) as a function of time. There will be a constant of integration, which you can evaluate by observing that s(0)=0.
- Hollywood
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