Answer:
(a). (i) [tex]-38\ \frac{ft}{s}[/tex]; (ii) [tex]-31.6\ \frac{ft}{s}[/tex]; (iii)[tex]-30.8\ \frac{ft}{s}[/tex]; (iv) [tex]-30.16\ \frac{ft}{s}[/tex]
(b). [tex]-30\ \frac{ft}{s}[/tex]
Step-by-step explanation:
The formula you need to use is:
[tex]V_{avg}=\frac{y_2-y_1}{t_2-t_1}[/tex]
Then, in this case:
[tex]V_{avg}=\frac{(34t_2 -16(t_2)^2)-(34t_1 - 16(t_1)^2)}{t_2-t_1}[/tex]
(a) Susbtituting values, we get:
(i) [tex]V_{avg}=\frac{(34(2.5) - 16(2.5)^2)-(34(2)- 16(2)^2)}{2.5-2})=-38\ \frac{ft}{s}[/tex]
(ii) [tex]V_{avg}=\frac{(34(2.1) - 16(2.1)^2)-(34(2)- 16(2)^2)}{2.5-2})=-31.6\ \frac{ft}{s}[/tex]
(iii) [tex]V_{avg}=\frac{(34(2.05) - 16(2.05)^2)-(34(2)- 16(2)^2)}{2.5-2})=-30.8\ \frac{ft}{s}[/tex]
(iv) [tex]V_{avg}=\frac{(34(2.01) - 16(2.01)^2)-(34(2)- 16(2)^2)}{2.5-2})=-30.16\ \frac{ft}{s}[/tex]
(b) Observe that as the time after 2 second gets smaller, the average velocity gets closer to [tex]-30\ \frac{ft}{s}[/tex]. Therefpre, we can can estimate that the instantaneous velocity when [tex]t = 2[/tex] is:
[tex]V=-30\ \frac{ft}{s}[/tex]
