What a wonderful website this is. Thank you all in advance for any help or guidance you can give me.
Find the distance traveled in 15 seconds by an object moving at a velocity of v(t) = 20 + 7 cos t feet per second.
Again, thank you for any help. I have no idea what to do with the cosine.
Edit: You know, I put this here because I was told it had to do with integrals? It might fit better in Trigonometry though. Sorry about that!
No, it doesn't seem so.
The problem is that I'm taking this AP Calculus class online [bad idea, for the record], and the online book really is not helpful at all. It hasn't actually talked about integrals or anything, and I certainly don't really remember them from two years ago. So I'm pretty much on my own. Thank you so much, though.
It MAY seem logical to assume one means the first 15 seconds.
The integral on [0,15] gives 300 + 7*sin(15) = 304.552
Unfortunately, it may NOT be a logical assumption. If we don't start watching for five seconds, the integral on [5,20] gives 300 + 7(sin(20)-sin(5)) = 313.103
We could play this game for a long time. One needs those initial conditions or some other guidance as to when or where we are clocking the 15 seconds.
In any case, you can estimate the answer well enough.
The constant "20" is, well, constant. It ALWAYS manages 300 in 15 seconds. The tricky part is the cosine, as you said. Interestingly, the cosine is periodic. Every it has gotten you nowhere. In this way, we can eliminate some of the cosine problem. . This means you really have to worry only about the last 2.434 seconds of the trip, since the previous seconds didn't get us anywhere! Of course, you still have to know where to start or stop. Just any 15 seconds will not due. We need to know which ones to watch.