The position of a body moving along x-axis at time t is given by `x= (t^(2)-4t+6)m`. The velocity of the body at time t = 3s is

Options

A. 2 m/s
B. 2.5 m/s
C. 3 m/s
D. 5 m/s

Answer

To find the velocity of the body at time \( t = 3 \) seconds, we will follow these steps:

### Step 1: Write down the position function
The position of the body is given by the equation:
\[ x(t) = t^2 - 4t + 6 \]

### Step 2: Differentiate the position function to find the velocity function
Velocity is defined as the derivative of the position with respect to time. Thus, we need to differentiate \( x(t) \):
\[ v(t) = \frac{dx}{dt} = \frac{d}{dt}(t^2 - 4t + 6) \]

### Step 3: Perform the differentiation
Using the power rule of differentiation:
- The derivative of \( t^2 \) is \( 2t \).
- The derivative of \( -4t \) is \( -4 \).
- The derivative of the constant \( 6 \) is \( 0 \).

So, we have:
\[ v(t) = 2t - 4 \]

### Step 4: Substitute \( t = 3 \) seconds into the velocity function
Now, we will find the velocity at \( t = 3 \):
\[ v(3) = 2(3) - 4 \]

### Step 5: Calculate the velocity
Calculating the above expression:
\[ v(3) = 6 - 4 = 2 \text{ m/s} \]

### Final Answer
The velocity of the body at time \( t = 3 \) seconds is \( 2 \text{ m/s} \).

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