Question

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.

Answer 1

Answer:

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.