The displacement x of an object is given as a funstion of time, `x=2t+3t^(2)`. The instantaneous velocity of the object at t = 2 s is

Options

A. `16 ms^(-1)`
B. `14 ms^(-1)`
C. `10 ms^(-1)`
D. `12 ms^(-1)`

Explanation

To find the instantaneous velocity of the object at \( t = 2 \) seconds, we will follow these steps:

### Step 1: Write down the displacement function
The displacement \( x \) of the object is given by the equation:
\[ x = 2t + 3t^2 \]

### Step 2: Differentiate the displacement function with respect to time
To find the instantaneous velocity, we need to differentiate the displacement function \( x \) with respect to time \( t \):
\[ v = \frac{dx}{dt} = \frac{d}{dt}(2t + 3t^2) \]

### Step 3: Apply the differentiation
Using the power rule of differentiation:
- The derivative of \( 2t \) is \( 2 \).
- The derivative of \( 3t^2 \) is \( 6t \).

Thus, the instantaneous velocity \( v \) is:
\[ v = 2 + 6t \]

### Step 4: Substitute \( t = 2 \) seconds into the velocity equation
Now, we will substitute \( t = 2 \) seconds into the velocity equation:
\[ v = 2 + 6(2) \]

### Step 5: Calculate the value
Calculating the above expression:
\[ v = 2 + 12 = 14 \text{ m/s} \]

### Final Answer
The instantaneous velocity of the object at \( t = 2 \) seconds is:
\[ \boxed{14 \text{ m/s}} \]

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