Answer:
The average speed of the object is 18.67 ft/s.
Step-by-step explanation:
Given;
height function, f(t) = -16t² + 42t + 5
The average speed is given by ;
[tex]v = \frac{dx}{dt} \\\\h(t) = -16t^2+42t+5\\\\h(1.5)= -16(1.5)^2 + 42(1.5)+5 = 32 \ ft\\\\[/tex]
from 1.5 s to 2.25 s = 0.75 s,
[tex]h(0.75)= -16(0.75)^2 + 42(0.75)+5 = 27.5 \ ft[/tex]
[tex]h(2.25)= 27.5 +(-16(2.25)^2 + 42(2.25)+5) \\\\h(2.25) = 27.5 + 18.5 = 46 \ ft[/tex]
The average speed is given by ;
[tex]v = \frac{h(2.25) - h(1.5)}{2.25-1.5}\\\\v = \frac{46-32}{0.75}\\\\v = 18.67 \ ft/s[/tex]
Therefore, the average speed of the object is 18.67 ft/s.
