If A is the area of this circle as a function of the radius, find A o f and interpret it.

Question

A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60 cm/s.

(a) Express the radius r of this circle as a function of the time t ( in seconds).
(b) If A is the area of this circle as a function of the radius, find A o f
and interpret it.

Answer 1

Step 1:

Circular ripple travels outward with a speed of 60 cm/sec.

(a)

Consider time taken by the circular ripple to travel a distance  is .

Speed-distance relation:

The distance travelled by the circular ripple is

Step 2:

(b)

Find .

Area of circle is .

Area of circular ripple is sq-cm.

Solution:

(a) The distance travelled by the circular ripple is .

(b) Area of circular ripple is sq-cm.