Calculate the amount of current passing through a wire at t=9 s, if the electric charge passing through a cross section of wire in t time is given as `q(t)=7t^2+9t-2`.

Answer

To calculate the amount of current passing through a wire at \( t = 9 \) seconds, given the electric charge \( q(t) = 7t^2 + 9t - 2 \), we can follow these steps:

### Step 1: Understand the relationship between charge and current
Current \( I \) is defined as the rate of flow of charge. Mathematically, this is expressed as:
\[ I(t) = \frac{dq}{dt} \]
where \( I(t) \) is the current at time \( t \) and \( q(t) \) is the charge at time \( t \).

### Step 2: Differentiate the charge function
We need to differentiate the given charge function \( q(t) = 7t^2 + 9t - 2 \) with respect to time \( t \):
\[ \frac{dq}{dt} = \frac{d}{dt}(7t^2 + 9t - 2) \]
Using the power rule of differentiation:
\[ \frac{dq}{dt} = 14t + 9 \]

### Step 3: Substitute \( t = 9 \) seconds into the current equation
Now we will substitute \( t = 9 \) into the current equation we derived:
\[ I(9) = 14(9) + 9 \]

### Step 4: Calculate the current
Now, perform the calculations:
\[ I(9) = 126 + 9 = 135 \, \text{A} \]

### Final Answer
Thus, the amount of current passing through the wire at \( t = 9 \) seconds is:
\[ \boxed{135 \, \text{A}} \]

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