Given the angular distance equation 0 = 2t3 – 3t2, the angular acceleration at t = 1 sec. is __________________?
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Answer: C. 6 rad/sec2
Explanation
Angular acceleration is the second derivative of angular displacement. Differentiating the displacement equation twice yields the acceleration function. Substituting one second into the acceleration equation results in six. Calculus relates displacement, velocity, and acceleration through differentiation. First derivatives of position functions yield instantaneous velocity values. Second derivatives determine instantaneous acceleration rates for moving bodies.
Kinematic equations using calculus model complex non-uniform rotational machinery. Engineers analyze displacement functions to predict peak mechanical stress points. Calculus applications are essential for solving advanced dynamics problems. One rad per second squared miscalculates the derivative evaluation steps. Four rad per second squared results from arithmetic errors in differentiation. Twelve rad per second squared forgets to complete the final algebraic substitution.
- Subject
- Engineering
- Category
- Civil Engineering
- Topic
- —
- Difficulty
- medium
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