A particle moves in a circular path of radius . Its speed , at time is given by . What is the magnitude of the tangential acceleration of the particle at ?
The given information is in SI units. State your answer in SI units too.
This problem is part of the set - Circular Motion Practice
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The tangential acceleration of a particle moving in a circular path is d t d v , that is the derivative of speed of the particle with respect to time. In the problem,
a T = d t d v = 6 4 π cos ( 6 π t )
When t = 5 , a T = 6 4 π cos ( 6 5 π ) = 6 4 π × 2 − 3 .
The magnitude of tangential acceleration is ∣ a T ∣ = 6 4 π × 2 3 ≈ 1 . 8 1 4 □