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
![\frac{dv}{ds} =-19/39\\m=\frac{dv}{ds}\\Hence\\v=ms+c\\](https://tex.z-dn.net/?f=%5Cfrac%7Bdv%7D%7Bds%7D%20%3D-19%2F39%5C%5Cm%3D%5Cfrac%7Bdv%7D%7Bds%7D%5C%5CHence%5C%5Cv%3Dms%2Bc%5C%5C)
where c=19
![v=-\frac{19}{39} *s+19\\](https://tex.z-dn.net/?f=v%3D-%5Cfrac%7B19%7D%7B39%7D%20%2As%2B19%5C%5C)
when s=8 we have
![v=-\frac{19}{39} * 8 +19\\v=15.1 m/s](https://tex.z-dn.net/?f=v%3D-%5Cfrac%7B19%7D%7B39%7D%20%2A%208%20%2B19%5C%5Cv%3D15.1%20m%2Fs)
hence a can be found by the chain rule
![a=\frac{ds}{dt} \frac{dv}{ds}\\a=v*\frac{dv}{ds}\\a=15.1 *-\frac{19}{39}\\a=7.357 m/s^2](https://tex.z-dn.net/?f=a%3D%5Cfrac%7Bds%7D%7Bdt%7D%20%5Cfrac%7Bdv%7D%7Bds%7D%5C%5Ca%3Dv%2A%5Cfrac%7Bdv%7D%7Bds%7D%5C%5Ca%3D15.1%20%2A-%5Cfrac%7B19%7D%7B39%7D%5C%5Ca%3D7.357%20m%2Fs%5E2)
From the equation
![v=-\frac{19}{39} *s+19\\](https://tex.z-dn.net/?f=v%3D-%5Cfrac%7B19%7D%7B39%7D%20%2As%2B19%5C%5C)
the s in term of t can be found
![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](https://tex.z-dn.net/?f=v%3D%5Cfrac%7Bds%7D%7Bdt%7D%20%5C%5C%5Cint%5Climits%20%7Bv%7D%20%5C%2C%20dt%20%3D%5Cint%5Climits%20%7B%7D%20%5C%2C%20ds%5C%5C%5Cint%5Climits%20%7B-%5Cfrac%7B19%7D%7B39%7D%20%2As%2B19%7D%20%5C%2C%20dt%3D%5Cint%5Climits%20%7B%7D%20%5C%2C%20ds%5C%5C%5C%5C%5Cint%5Climits%5Et_0%20%7B%7D%20%5C%2C%20dt%3D%5Cint%5Climits%5Es_0%20%7B%5Cfrac%7B1%7D%7B-%5Cfrac%7B19%7D%7B39%7D%20%2As%2B19%7D%20%7D%20%5C%2C%20ds)
![t=-\frac{39}{19} ln(\frac{s-39}{39} )\\](https://tex.z-dn.net/?f=t%3D-%5Cfrac%7B39%7D%7B19%7D%20ln%28%5Cfrac%7Bs-39%7D%7B39%7D%20%29%5C%5C)
Hence it can be seen that if s approaches 39 the t function becomes undefined hence s is never 39m
Answer:
seasonl changes at the poles only
Explanation:
Yes they do. A crystalline pattern as other ionic compounds have
So obviously the 20N pulls more than the 5N. Friction opposes direction of motion, so the 5N opposes the 20N and the two forces are against each other.
Net force would be in the direction of the 20N force: 20N - 5N = 15N.
Force = mass*acceleration
15 = (5)*acceleration
acceleration = 3m/s^2