Question

The distance \( s \) traveled by a particle in time \( t \) is given by: $$ s = 4t^2 + 2t + 3. $$ The velocity of the particle when \( t = 3 \) seconds is: 

• A. \( 26 \) unit/sec
• B. \( 20 \) unit/sec
• C. \( 24 \) unit/sec
• D. \( 30 \) unit/sec

Hint:

Velocity is the first derivative of displacement with respect to time.

Answer 1

The Correct Option is A

Step 1: Finding velocity by differentiation \[ v = \frac{ds}{dt} = \frac{d}{dt} (4t^2 + 2t + 3). \] \[ v = 8t + 2. \] Step 2: Substituting \( t = 3 \) \[ v = 8(3) + 2 = 24 + 2 = 26. \]

Answer 2

Given:
\[ s = 4t^2 + 2t + 3 \] where \( s \) is the distance traveled by the particle in time \( t \).

Step 1: Velocity \( v \) is the derivative of distance \( s \) with respect to time \( t \):
\[ v = \frac{ds}{dt} = \frac{d}{dt} (4t^2 + 2t + 3) = 8t + 2 \]

Step 2: Calculate velocity at \( t = 3 \):
\[ v = 8 \times 3 + 2 = 24 + 2 = 26 \]

Therefore, the velocity of the particle at \( t = 3 \) seconds is:
\[ \boxed{26 \text{ unit/sec}} \]