Calculus Based Questions: Practice Problem & Solution
Motion of a particle is given by equation \(S = 3t^3 + 7t^2 + 14t + 8\text{m}\). The value of acceleration of the particle at \(t = 1 \text{ sec}\) is: (2000)
Solution Explained:
To solve this problem, we apply the core principles of Calculus Based Questions. Understanding the underlying formula is key to arriving at the correct answer below:
Given \(S = 3t^3 + 7t^2 + 14t + 8\). Velocity \(v = \frac{dS}{dt} = 9t^2 + 14t + 14\). Acceleration \(a = \frac{dv}{dt} = 18t + 14\). At \(t=1 \text{ s}\), \(a = 18(1) + 14 = 32 \text{ m/s}^2\).
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