Calculus help : Othor Games

» Tue May 17, 2011 10:23 am

I'm terrible at related rates and could use some help. This problem specifically.

The volume of unmelted ice (in cubic inches) remaining from a melting ice cube after t seconds is given by V(t) = 2000 - 40t + 0.2t^2

At what rate is the volume changing when t=40 seconds?

And another one (not related rates):

A particle travels in a straight line with constant acceleration of 3m/sec^2. If the velocity is 10m/s at t=2, how far does the particle travel during the time when the velocity increases from 4 m/s to 10 m/s?

Thanks guys.

EDIT: I'd do it myself but I don't even know where to start. Just looking for someone to point me in the right direction.

» Tue May 17, 2011 3:13 am

What are you getting stuck on? How have you tried to solve it so far and what are you getting?

» Tue May 17, 2011 12:34 am

First one, you take the derivative of T.

So we toss out the 2000.

We kick the 't' of the negative -40.

And we then power rule the .2t^2 so it becomes .4t.

So you get dV(t)/dt=-40+0.4t

Plug and Chug.

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2nd one:

Integral of Acceleration is velocity.
Integral of Velocity is distance traveled.

Since we know V=10m/s at t=2, so we can backtrack and get V=4m/s at t=0.

Therefore V(t)=3t+4.

Taking the integral and power ruling it again...

X(t)=1.5t^2+4t.

Now that we have our equations, we can use V(t)=3t+4 to get the time V=4m/s and V=10m/s (t=0 and t=2, ironically enough). Those are the bounds of the integral.

And Plug and chug.