Question

A particle moves with velocity ($v = 3t^2 + 2t$). Find acceleration at ($t = 2$) s. ____.

• A. 14 m/s²
• B. 12 m/s²
• C. 16 m/s²
• D. 10 m/s²

Hint:

Always check if the question gives you Displacement ($x$) or Velocity ($v$). If $x$ is given, you must differentiate twice to find acceleration. If $v$ is given, you only differentiate once.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Acceleration is defined as the instantaneous rate of change of velocity with respect to time. Mathematically, it is the first derivative of the velocity function.

Step 2: Key Formula or Approach:
\[ a = \frac{dv}{dt} \]

Step 3: Detailed Explanation:
Given: $v = 3t^2 + 2t$. 1. Differentiate $v$ with respect to $t$: \[ a = \frac{d}{dt}(3t^2 + 2t) \] \[ a = 6t + 2 \] 2. Substitute $t = 2$ into the acceleration equation: \[ a = 6(2) + 2 \] \[ a = 12 + 2 = 14 \text{ m/s²} \]

Step 4: Final Answer:
The acceleration at $t = 2$ s is 14 m/s².