Answer:
The relationship between the initial stored energy
and the stored energy after the dielectric is inserted
is:
c) 
Explanation:
A parallel plate capacitor with
that is connected to a voltage source
holds a charge of
. Then we disconnect the voltage source and keep the charge
constant . If we insert a dielectric of
between the plates while we keep the charge constant, we found that the potential decreases as:

The capacitance is modified as:

The stored energy without the dielectric is
The stored energy after the dielectric is inserted is:

If we replace in the above equation the values of V and C we get that


Finally

To solve this problem we will apply the concepts related to the conservation of kinetic energy and elastic potential energy. Thus we will have that the kinetic energy is

And the potential energy is

Here,
m = mass
v = Velocity
x = Displacement
k = Spring constant
There is equilibrium, then,
KE = PE

Our values are given as,

Replacing we have that


Therefore the speed of the cart is 2.19m/s