Answer:
57.5022228905 s
Explanation:
[tex]V_i[/tex] = Initial voltage
[tex]V_f[/tex] = Final voltage = 0.401 V
[tex]t_1[/tex] = Initial time = 8.36 s
[tex]t_2[/tex] = Final time
K = Kinetic Energy = [tex]3.18\times 10^{-8}\ J[/tex]
C = Charge = [tex]3.74\times 10^{-6}\ C[/tex]
Voltage is given by
[tex]V=\dfrac{K}{C}\\\Rightarrow V=\dfrac{3.17\times 10^{-8}}{3.74\times 10^{-6}}\\\Rightarrow V=0.00847593582888\ V[/tex]
We have the relation
[tex]\dfrac{V_i}{V_f}=(\dfrac{t_i}{t_f})^2\\\Rightarrow t_f=\sqrt{\dfrac{t_i^2V_f}{V_i}}\\\Rightarrow t_f=\sqrt{\dfrac{8.36^2\times 0.401}{0.00847593582888}}\\\Rightarrow t_f=57.5022228905\ s[/tex]
The time taken is 57.5022228905 s
