A particle is moving on a straight line with velocity (v) as a function of time (t) according to relation `v = (5t^(2) - 3t + 2)m//s` . Now give the answer of following questions :
Velocity of particle at t = 3 sec. is :

Options

A. `30 m//s`
B. `38 m//s`
C. `22 m//s`
D. `36 m//s`

Explanation

To find the velocity of the particle at \( t = 3 \) seconds, we will substitute \( t = 3 \) into the given velocity function:

1. **Write down the velocity function**:
\[ v(t) = 5t^2 - 3t + 2 \]

2. **Substitute \( t = 3 \) into the velocity function**:
\[ v(3) = 5(3^2) - 3(3) + 2 \]

3. **Calculate \( 3^2 \)**:
\[ 3^2 = 9 \]

4. **Substitute \( 9 \) back into the equation**:
\[ v(3) = 5(9) - 3(3) + 2 \]

5. **Calculate \( 5(9) \)**:
\[ 5(9) = 45 \]

6. **Calculate \( 3(3) \)**:
\[ 3(3) = 9 \]

7. **Now substitute these values back into the equation**:
\[ v(3) = 45 - 9 + 2 \]

8. **Perform the subtraction and addition**:
\[ v(3) = 45 - 9 = 36 \]
\[ v(3) = 36 + 2 = 38 \]

9. **Final answer**:
\[ v(3) = 38 \, \text{m/s} \]