The formula for current is:

i = dq/dt (where i=current, q=charge, t=time)

the equation for q is given in the questions as:

*q* = *3t*^{3} + 6*t* + 6,

and t = 0.9 s

To find the current we take the derivative of q with respect to time, then plug in t.

so

i = 9t^2 + 6

Now plug in t = 0.9s

i = 9(0.9s)^2 + 6 = 13.29 A

i = 13.29 A

Part B, the value of current density is equal to the current divided by the area

Area = 1.95 cm^2 = 1.95*10^-4 m^2

current = 13.29 A

So current density is:

current density = 13.29 A / 1.95*10^-4 m^2 = 68153 A/m^2 = 68.15 kA/m^2

So current density is 68.15 kA/m^2