Answer
(a) 80 ft/sec
(b) 0.0125 sec/ft. This tells us that the pace of the car skid was 0.0125 sec/ft.
Explanation
Given function:
Where v is the velocity, g is the acceleration due to gravity (32 ft/sec²), d is the length, and f is the friction coefficient of the surface.
(a) The how fast, v(d) the car travel was traveling when it lost control can be calculated by putting g = 32 ft/sec², f = 0.5 and d = 200 ft into the given function:
[tex]\begin{gathered} v(d)=\sqrt{2\times32\times0.5\times200} \\ \\ v(d)=\sqrt{6400} \\ \\ v(d)=80\text{ }ft\text{/}sec \end{gathered}[/tex]
(b) The inverse of the function v(d) is:
[tex]\frac{1}{v(d)}[/tex]
From part a, v(d) = 80 ft/sec, therefore, the inverse is:
[tex]\frac{1}{v(d)}=\frac{1}{80\text{ }ft\text{/}sec}=0.0125\text{ }sec\text{/}ft[/tex]
This tells us that the pace of the car skid was 0.0125 sec/ft.
