On the moon, all free-fall distance functions are of the form s(t)equals=0.810.81tsquared2, where t is in seconds and s is in meters. An object is dropped from a height of 150150 meters above the moon. After 88 sec, consider parts (a) through (d) below. a) How far has the object fallen? b) How fast is it traveling? c) What is its acceleration? d) Explain the meaning of the second derivative of this free-fall function.

Check Explanation.

Step-by-step explanation:

s(t) = 0.810t²

a) Distance fallen through, just after t = 8 s

s(8) = 0.810(8²) = 51.84 m

b) Velocity of the body, just after t = 8 s

s(t) = 0.810t²

v(t) = (ds/dt) = 1.620t

v(8) = 1.62(8) = 12.96 m/s

c) Acceleration of the body, just after t = 8 s

v(t) = 1.620t

a(t) = (dv/dt) = 1.620

a(8) = 1.620 m/s²

d) The answer obtained from the 2nd derivative of this free fall function for acceleration is a constant.

This means, the acceleration of the body is constant regardless of the time.

The body undergoing the motion described by the free fall function has a constant acceleration.

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