Please help in this problem.. Here's the problem:
A body rises vertically from earth according to the law S= 64t - 16t^2. In here, I need to show or prove that it has lost one-half its velocity in the first 48ft. Of rise.

Another thing.. can you please check if my answer in this problem is correct.. :)
A particle is moving along a horizontal line according to the formula S= 1/3 t^3 - 1/2 t^2 - 2t + 2 whose S feet is the distance of the particle from the origin at time t(secs).
a.) what is the instantaneous velocity of the particle at t=2?
my answer: v=0
b.) when is the particle is at rest? When v=0, t>2 and t>-1
c.) when is the particle moving to the right? When v>0.

Hope you can help me. Thanks a lot.

I'm going to assume that you know a bit of calculus - if not, please post back and we'll try to do these a different way:

For the first problem, take the derivative of s(t) and you get v(t) = s'(t) = 64 - 32t. Its initial velocity at t = 0 is therefore v(0) = 64 - 32*0 = [EDIT] 64 ft/sec. So the question is, when does v(t) = half of that, or [EDIT] 32 ft/s?

v(t) = 64 - 32t = [EDIT] 32, solve for t.

Then shove that value for t back into the original equation for s(t) to find how far the body has risen at the point in time when it is moving at [EDIT] 32 ft/s.

For the others:

a) Correct
b) The body is at rest precisely at t= 2 or t = -1. Why did you put in the inequality signs?
c) Yes, the particle moves to theright when when v>0, but I suspect that they want the answer in terms of time. So, for what values of t is v>0?

Ok! I knew now how to solve it.. thanks! :)

Wait.. The question in the first problem is that I need to show that in the first 48ft rise of the body, it has lost one-half of its velocity..

Wait.. The question in the first problem is that I need to show that in the first 48ft rise of the body, it has lost one-half of its velocity..

My apologies - but I see I made a bit of a careless math error in my initial response. I have edited my response (as indicated by the [EDIT] notations). Sorry for the confusion. What I hope you can see is that this method shows that at the same instant that the body has lost half its velocity it has risen 48 ft, which is what the question asked for.