A feather dropped on the moon On the moon, a feather will fall to the ground at the same rate as a heavy stone. Suppose a feather is dropped from a height of 40 m above the surface of the moon. Its height (in meters) above the ground after t seconds is s = 40−0.8t². Determine the velocity and acceleration of the feather the moment it strikes the surface of the moon.

Verified step by step guidance

1. Step 1: Identify the function for the height of the feather, which is given as s(t) = 40 - 0.8t^2, where s is the height in meters and t is the time in seconds.
2. Step 2: To find the velocity of the feather, take the first derivative of the height function s(t) with respect to time t. This will give you the velocity function v(t).
3. Step 3: Calculate the first derivative: v(t) = ds/dt = d/dt (40 - 0.8t^2).
4. Step 4: To find the acceleration of the feather, take the second derivative of the height function s(t) with respect to time t. This will give you the acceleration function a(t).
5. Step 5: Calculate the second derivative: a(t) = d^2s/dt^2 = d/dt (v(t)).