A motorcycle has a constant acceleration of 3.49 m/s2. Both the velocity and acceleration of the motorcycle point in the same di
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Answer:
The distance is
Explanation:
From the question we are told that
The initial speed of the electron is
The mass of electron is
Let be the distance between the electron and the proton when the speed of the electron instantaneously equal to twice the initial value
Let be the initial kinetic energy of the electron \
Let be the kinetic energy of the electron at the distance
from the proton
Considering that energy is conserved,
The energy at the initial position of the electron = The energy at the final position of the electron
i.e
are the potential energy at the initial position of the electron and at distance d of the electron to the proton
Here
So the equation becomes
Here are the charge on the electron and the proton and their are the same since a charge on an electron is equal to charge on a proton
is electrostatic constant with value
i.e
is the velocity at distance d from the proton = 2
So the equation becomes
Making d the subject of the formula
The energy stored by a system of capacitors is given by
where Ceq is the equivalent capacitance of the system, and V is the voltage applied.
In the formula, we can see there is a direct proportionality between U and C. This means that if we want to increase the energy stored by 4 times, we have to increase C by 4 times, if we keep the same voltage.
Calling
the capacitance of the original capacitor, we can solve the problem by asking that, adding a new capacitor with 
, the new equivalent capacitance of the system 
must be equal to 
. If we add the new capacitance X in parallel, the equivalent capacitance of the new system is the sum of the two capacitance
and since Ceq must be equal to 4 C1, we can write
from which we find
where Ceq is the equivalent capacitance of the system, and V is the voltage applied.
In the formula, we can see there is a direct proportionality between U and C. This means that if we want to increase the energy stored by 4 times, we have to increase C by 4 times, if we keep the same voltage.
Calling
and since Ceq must be equal to 4 C1, we can write
from which we find