Answer:
Explanation:The rate of decrease of velocity is given with respect to displacement. As v approaches zero when s approaches 39, it can be written as
[tex]\frac{dv}{ds} =-19/39\\m=\frac{dv}{ds}\\Hence\\v=ms+c\\[/tex]
where c=19
[tex]v=-\frac{19}{39} *s+19\\[/tex]
when s=8 we have
[tex]v=-\frac{19}{39} * 8 +19\\v=15.1 m/s[/tex]
hence a can be found by the chain rule
[tex]a=\frac{ds}{dt} \frac{dv}{ds}\\a=v*\frac{dv}{ds}\\a=15.1 *-\frac{19}{39}\\a=7.357 m/s^2[/tex]
From the equation
[tex]v=-\frac{19}{39} *s+19\\[/tex]
the s in term of t can be found
[tex]v=\frac{ds}{dt} \\\int\limits {v} \, dt =\int\limits {} \, ds\\\int\limits {-\frac{19}{39} *s+19} \, dt=\int\limits {} \, ds\\\\\int\limits^t_0 {} \, dt=\int\limits^s_0 {\frac{1}{-\frac{19}{39} *s+19} } \, ds[/tex]
[tex]t=-\frac{39}{19} ln(\frac{s-39}{39} )\\[/tex]
Hence it can be seen that if s approaches 39 the t function becomes undefined hence s is never 39m
