Help with derivitive word problems

[jarettbrock]

1. A stone is dropped into a lake, creating a circular ripple ripple that travels outward at a speed of 60 cm/s. Find the rate at which the area within the circle is increasing after (a) 1 s, (b) 3 s, (c) 5 s. What can you conclude?

what i've done with this is find the first two derivitives of the area of a circle, but i am not sure what to do from there, and i'm not sure where the 60 m/s come in.

 

[tkhunny]

Why do you need two derivatives?

\(\displaystyle Area(t) = \pi Radius(t)^{2}\)

\(\displaystyle dArea/dt = \pi (2 \cdot Radius(t)) dRadius/dt\)

That's all the calculus you need. The rest is algebra.

dRadius/dt is given.

Radius(t) is easily calculated.

You're done.

 

[jarettbrock]

Well we are taught that the first derivitive of the function is the velocity and the second derivitive is the acceleration. You dont need the acceleration in the problem but i am almost positive you need the velocity derivitive.

 

[jarettbrock]

so basically i just start pluggin those values into the derivitives? Because that is what i did but it seems too simple.