Answer:
a. ![t=19.56 s](https://tex.z-dn.net/?f=t%3D19.56%20s)
b.![d=718.34](https://tex.z-dn.net/?f=d%3D718.34)
Explanation:
The solution to the differential equation
![\dfrac{dv}{dt}=9.8-\dfrac{v}{5}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdv%7D%7Bdt%7D%3D9.8-%5Cdfrac%7Bv%7D%7B5%7D)
is the exponential function
![v(t)=ce^{-0.2t}+49](https://tex.z-dn.net/?f=v%28t%29%3Dce%5E%7B-0.2t%7D%2B49)
and we find
from the initial condition ![v(0)=0:](https://tex.z-dn.net/?f=v%280%29%3D0%3A)
![0=ce^{-0.2*0}+49\\\\0=c+49\\\\c=-49](https://tex.z-dn.net/?f=0%3Dce%5E%7B-0.2%2A0%7D%2B49%5C%5C%5C%5C0%3Dc%2B49%5C%5C%5C%5Cc%3D-49)
Therefore, we have
![v(t)=-49e^{-0.2t}+49](https://tex.z-dn.net/?f=v%28t%29%3D-49e%5E%7B-0.2t%7D%2B49)
![\boxed{ v(t)=49(1-e^{-0.2t})}](https://tex.z-dn.net/?f=%5Cboxed%7B%20v%28t%29%3D49%281-e%5E%7B-0.2t%7D%29%7D)
Part A:
The maximum velocity that the object can reach is 49 (which the maximum value
can have).
Now, 98% of 49 is 48.02; therefore,
![48.02=49(1-e^{-0.2t})](https://tex.z-dn.net/?f=48.02%3D49%281-e%5E%7B-0.2t%7D%29)
![0.98=1-e^{-0.2t}](https://tex.z-dn.net/?f=0.98%3D1-e%5E%7B-0.2t%7D)
![e^{-0.2t}=0.02](https://tex.z-dn.net/?f=e%5E%7B-0.2t%7D%3D0.02)
![\boxed{t=19.56 s}](https://tex.z-dn.net/?f=%5Cboxed%7Bt%3D19.56%20s%7D)
Part B:
The distance traveled is the integral of the speed:
![d=\int_0^{19.56}v(t)*dt](https://tex.z-dn.net/?f=d%3D%5Cint_0%5E%7B19.56%7Dv%28t%29%2Adt)
![d=\int^{19.56}_0 {49(1-e^{-0.2t})} \, dt](https://tex.z-dn.net/?f=d%3D%5Cint%5E%7B19.56%7D_0%20%7B49%281-e%5E%7B-0.2t%7D%29%7D%20%5C%2C%20dt)
![d=49[t+5e^{-0.2t}]_0^{19.56}](https://tex.z-dn.net/?f=d%3D49%5Bt%2B5e%5E%7B-0.2t%7D%5D_0%5E%7B19.56%7D)
![\boxed{d=718.34}](https://tex.z-dn.net/?f=%5Cboxed%7Bd%3D718.34%7D)
The correct answer would be the letter B.) NaF this attracts opposite charges. The final formula of sodium fluoride would be NaF it’s <span>compound is formed by the complete transfer of electrons from a metal to a nonmetal.</span>
Answer:
Explanation: When you throw a ball up in the air, its direction/velocity on the way up, although it rises up into the air, is actually downward. On its way up, its speed decreases, until it momentarily stops at the very top of the ball s motion. Its acceleration is -9.8 m/s^2 at the very top.
Inertia is the tendency of an object to resist a change in its motion.