Answer:
a) velocity v = 322.5m/s
b) time t = 19.27s
Explanation:
Note that;
ads = vdv
where
a is acceleration
s is distance
v is velocity
Given;
a = 6 + 0.02s
so,
![\int\limits^s_0 {a} \, ds = \int\limits^v_0 {v} \, dv\\ \int\limits^s_0 {6+0.02s} \, ds = \int\limits^v_0 {v} \, dv\\ 6s + \frac{0.02s^{2} }{2} = \frac{1}{2} v^{2} \\v = \sqrt{12s + 0.02s^{2} } .....................1 \\\\\\](https://tex.z-dn.net/?f=%5Cint%5Climits%5Es_0%20%7Ba%7D%20%5C%2C%20ds%20%20%3D%20%5Cint%5Climits%5Ev_0%20%7Bv%7D%20%5C%2C%20dv%5C%5C%20%5Cint%5Climits%5Es_0%20%7B6%2B0.02s%7D%20%5C%2C%20ds%20%20%3D%20%5Cint%5Climits%5Ev_0%20%7Bv%7D%20%5C%2C%20dv%5C%5C%206s%20%2B%20%5Cfrac%7B0.02s%5E%7B2%7D%20%7D%7B2%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20v%5E%7B2%7D%20%5C%5Cv%20%3D%20%5Csqrt%7B12s%20%2B%200.02s%5E%7B2%7D%20%7D%20.....................1%20%5C%5C%5C%5C%5C%5C)
Remember that
![v = \frac{ds}{dt} \\\frac{ds}{v} = dt\\\int\limits^s_0 {\frac{ds}{\sqrt{12s+0.02s^{2} } } } \, ds = \int\limits^t_0 {} \, dt \\t= (5\sqrt{2} ) ln \frac{| [s + 300 + \sqrt{(s^{2} + 600s)} ] |}{300} .......2](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7Bds%7D%7Bdt%7D%20%5C%5C%5Cfrac%7Bds%7D%7Bv%7D%20%3D%20dt%5C%5C%5Cint%5Climits%5Es_0%20%7B%5Cfrac%7Bds%7D%7B%5Csqrt%7B12s%2B0.02s%5E%7B2%7D%20%7D%20%7D%20%7D%20%5C%2C%20ds%20%3D%20%5Cint%5Climits%5Et_0%20%7B%7D%20%5C%2C%20dt%20%5C%5Ct%3D%20%20%285%5Csqrt%7B2%7D%20%29%20ln%20%20%5Cfrac%7B%7C%20%5Bs%20%2B%20300%20%2B%20%5Csqrt%7B%28s%5E%7B2%7D%20%20%2B%20600s%29%7D%20%5D%20%7C%7D%7B300%7D%20.......2)
substituting s = 2km =2000m, into equation 1
v = 322.5m/s
substituting s = 2000m into equation 2
t = 19.27s
It reaches 10 or 20 million degrees kelvin but it can get as high as 10 million degrees kelvin
Answer: In order to help improve your fitness levels you can swim, jog/run, body weight exercises, and a balanced diet. Explain why the greatest benefits to cardiorespiratory fitness come from sustained physical activities like running, walking and cycling.
Explanation:
Answer:
c) 12
Explanation:
A Solar eclipse occurs when The Sun, The Earth and The Moon comes in a straight line with the Moon being in between the Earth and the Sun. At this point the Moon appears to block the Sun and Moon's shadow falls on Earth. This would occur only on the day of the New Moon.
If the Moon's orbit was in the same plane as that of the Earth's orbit. Every new Moon, there would be a Solar Eclipse. The Lunar cycle is of 29.5 Days which means there will be one new Moon every month. So there will be 12 Solar Eclipses every year.
Currently, the orbit of the Moon is tilted at an angle of 5° thus we don't see that many Solar eclipses. Maximum of 5 solar eclipses can occur in an year.
Answer:
289282
Explanation:
r = Radius of plate = 0.52 mm
d = Plate separation = 0.013 mm
A = Area = ![\pi r^2](https://tex.z-dn.net/?f=%5Cpi%20r%5E2)
V = Potential applied = 2 mV
k = Dielectric constant = 40
= Electric constant = ![8.854\times 10^{-12}\ \text{F/m}](https://tex.z-dn.net/?f=8.854%5Ctimes%2010%5E%7B-12%7D%5C%20%5Ctext%7BF%2Fm%7D)
Capacitance is given by
![C=\dfrac{k\epsilon_0A}{d}](https://tex.z-dn.net/?f=C%3D%5Cdfrac%7Bk%5Cepsilon_0A%7D%7Bd%7D)
Charge is given by
![Q=CV\\\Rightarrow Q=\dfrac{k\epsilon_0AV}{d}\\\Rightarrow Q=\dfrac{40\times 8.854\times 10^{-12}\times\pi \times (0.52\times 10^{-3})^2\times 2\times 10^{-3}}{0.013\times 10^{-3}}\\\Rightarrow Q=4.6285\times 10^{-14}\ \text{C}](https://tex.z-dn.net/?f=Q%3DCV%5C%5C%5CRightarrow%20Q%3D%5Cdfrac%7Bk%5Cepsilon_0AV%7D%7Bd%7D%5C%5C%5CRightarrow%20Q%3D%5Cdfrac%7B40%5Ctimes%208.854%5Ctimes%2010%5E%7B-12%7D%5Ctimes%5Cpi%20%5Ctimes%20%280.52%5Ctimes%2010%5E%7B-3%7D%29%5E2%5Ctimes%202%5Ctimes%2010%5E%7B-3%7D%7D%7B0.013%5Ctimes%2010%5E%7B-3%7D%7D%5C%5C%5CRightarrow%20Q%3D4.6285%5Ctimes%2010%5E%7B-14%7D%5C%20%5Ctext%7BC%7D)
Number of electron is given by
![n=\dfrac{Q}{e}\\\Rightarrow n=\dfrac{4.6285\times 10^{-14}}{1.6\times10^{-19}}\\\Rightarrow n=289281.25\ \text{electrons}](https://tex.z-dn.net/?f=n%3D%5Cdfrac%7BQ%7D%7Be%7D%5C%5C%5CRightarrow%20n%3D%5Cdfrac%7B4.6285%5Ctimes%2010%5E%7B-14%7D%7D%7B1.6%5Ctimes10%5E%7B-19%7D%7D%5C%5C%5CRightarrow%20n%3D289281.25%5C%20%5Ctext%7Belectrons%7D)
The number of charge carriers that will accumulate on this capacitor is approximately 289282.