A particle translates along a linear path such that the displacement x covered in t seconds follows x = t^2(t - 4). Which differential equation defines the particle's acceleration_________________?
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Answer: C. 6f-8
Explanation
Differentiating the displacement equation twice with respect to time yields the exact differential equation for the particle's acceleration. First derivative of displacement with respect to time gives the velocity function of the moving particle. Second derivative of the polynomial displacement function produces the linear acceleration expression in terms of time. Kinematics defines velocity as the time rate of change of position and acceleration as the time rate of change of velocity. Expanding the polynomial x = t cubed minus four t squared simplifies the successive differentiation process. Calculus power rules allow straightforward derivation of velocity and acceleration equations from position functions.
Option A provides an incorrect algebraic expression that fails to match the correct second derivative result. Option B represents an erroneous derivative containing incorrect signs and coefficient values from polynomial expansion. Option D misses the correct coefficient for the linear time term during the second differentiation step.
- Subject
- Engineering
- Category
- Civil Engineering
- Topic
- —
- Difficulty
- medium
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