:-$ Calculus Based Physics: Newton's Laws Problem

[johnsonandrew]

The problem statement, all variables and given/known data
A robot working in a nuclear power plant moves along a straight track. If it experiences a force

F(t) = -Fi [ 1 + (4.0t - 2.0T)/T ]

where T is a constant with the units of time, what is the instantaneous speed of the robot at the very end of the interval 0 \leq t \leq T. It was at rest at t= 0

Relevant equations

ma = -Fi [ 1 + (4.0t - 2.0T)/T ]

\int a(t) = v(t)


How do I integrate that?? it will be a = [ -Fi [ 1 + (4.0t - 2.0T)/T ] ] / m
but how do I integrate with so many variables... do I plug in t for T? No mass given...

[HallsofIvy]

I'm sorry? "so many variables"? There is only one variable: t. Integrate with respect to t.

[cristo]

Your integral should be v=\int a dt +C for some constant. Now, you are correct in saying that a=[ -Fi [ 1 + (4.0t - 2.0T)/T ] ] / m. You are told in your question that T is a constant, so you should be able to integrate this expression, using the limits given.

[johnsonandrew]

Well I tried putting \int [ -Fi [ 1 + (4.0t - 2.0T)/T ] ] / m , t into my TI-89 and it didn't integrate. It simply returned " -\int [ Fi [ 1 + (4.0t - 2.0T)/Tm ] dt
I figured it couldn't be integrated since the calculator won't do it, and that I must have set it up wrong. I guess not. Is there any way I can get this to work on my calculator (on the TI-89)? I have not yet learned integration in my Calculus class, so for now those of us unable to do integration are expected to simply punch it in our calculators.

[cristo]

You should learn that there are some things that calculators cannot do; especially those things that one needs a brain for. I imagine there is a way to do it, but I don't own a graphic calculator so couldn't tell you. You would need to tell the calculator that T, Fi and m are constants, and that you are integrating wrt t.

However, if your teacher actually told you to use a calculator, and gave you this problem knowing full well you hadn't covered calculus, then I suggest you simply write the integral. Classes like this should not be telling students to use calculators instead of performing calculations by oneself.

[johnsonandrew]

No, you're right, and I understand that. I'd much rather know how to do the problem longhand. Unfortunately my high school is not big on physics, so the only AP course offered this year is calculus-based. The prerequisite for the class is only pre-calculus, not calculus, surprisingly. It only requires simultaneous enrollment in calculus. I wonder why that is, when they are giving us problems like this at the beginning of the year. We have only just finished covering derivatives, and that’s all. Oh well, thanks for your help, I'll let my teacher know and see what she says. :-s