Shrinking square The sides of a square decrease in length at a rate of 1 m/s.
a. At what rate is the area of the square changing when the sides are 5 m long?

Verified step by step guidance

1. Let the length of the side of the square be denoted as 's'. Since the sides are decreasing at a rate of 1 m/s, we can express this as ds/dt = -1 m/s.
2. The area 'A' of the square can be expressed in terms of the side length: A = s^2.
3. To find the rate of change of the area with respect to time, we need to differentiate the area with respect to time using the chain rule: dA/dt = dA/ds * ds/dt.
4. Calculate dA/ds, which is the derivative of A with respect to s: dA/ds = 2s.
5. Substitute s = 5 m and ds/dt = -1 m/s into the equation: dA/dt = 2(5)(-1).