Answer:
the capacitor voltage is V = 20 V
Explanation:
Given,
Capacitance of the capacitor = 2.0 μF
energy stored = 200 W
time (t) =2.0 μs
Capacitor voltage = ?
![\dfrac{dE}{dt}=200 W](https://tex.z-dn.net/?f=%5Cdfrac%7BdE%7D%7Bdt%7D%3D200%20W)
![E =200\times 2 \times 10^{-6}](https://tex.z-dn.net/?f=E%20%3D200%5Ctimes%202%20%5Ctimes%2010%5E%7B-6%7D)
![E =400 \times 10^{-6}\ J](https://tex.z-dn.net/?f=E%20%3D400%20%5Ctimes%2010%5E%7B-6%7D%5C%20J)
we know,
![E = \dfrac{1}{2}CV^2](https://tex.z-dn.net/?f=E%20%3D%20%5Cdfrac%7B1%7D%7B2%7DCV%5E2)
![V =\sqrt{\dfrac{2E}{C}}](https://tex.z-dn.net/?f=V%20%3D%5Csqrt%7B%5Cdfrac%7B2E%7D%7BC%7D%7D)
![V =\sqrt{\dfrac{2\times 400 \times 10^{-6}}{2\times 10^{-6}}}](https://tex.z-dn.net/?f=V%20%3D%5Csqrt%7B%5Cdfrac%7B2%5Ctimes%20400%20%5Ctimes%2010%5E%7B-6%7D%7D%7B2%5Ctimes%2010%5E%7B-6%7D%7D%7D)
![V =\sqrt{400}](https://tex.z-dn.net/?f=V%20%3D%5Csqrt%7B400%7D)
V = 20 V
so , the capacitor voltage is V = 20 V
A = 1.15m/s2, Vf = 80.0km/h --> we need it in m/s, so:
Vf = 80km/h × 1000m/1km × 1h/3600s
= 22.22m/s
Top speed = Vf, initial speed = Vi
time (t) = V(Vf-Vi) ÷ a
t = (22.22-0)m/s ÷ 1.15m/s2
t = 22.22m/s × s2/1.15m
= 19.32 seconds