Read the passage below and answer following questions.

The current through a wire depends on time as i=i₀​+3αt², where i₀​=10A and α = 0.5 ​A/sec².

What is the average current for the interval t = 0 to t = 2 s ?

12 A

$Charge , dq = Idt = (I_0 + 3\alpha t^2)dt $

$\text{Integrating both sides,}$

$ q = I_0​t+\alpha t^3$

$\text {At t = 2 s Average Current = Total charge/Total time}$

 $I_{av} = \frac{q}{t} = I_0+ \alpha t^2 = 10+0.5\times 2^2=12A$