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A particle moves in the x-y plane with velocity v = a i + (b t) j. At the instant t = a*sqrt(3)/b, find the magnitudes of the tangential acceleration, the normal (centripetal) acceleration, and the total acceleration.

1. aₜ = b*sqrt(3)/2, aₙ = b/2, a_total = b
2. aₜ = b/2, aₙ = b*sqrt(3)/2, a_total = b
3. aₜ = b, aₙ = b, a_total = b*sqrt(2)
4. aₜ = b*sqrt(3), aₙ = b, a_total = 2b

Correct answer: aₜ = b*sqrt(3)/2, aₙ = b/2, a_total = b

Solution

The acceleration is constant, a = b j with magnitude b; at the given instant the velocity makes 60 deg with the x-axis, so the component of a along v is aₜ = b sin60 = b*sqrt(3)/2 and the normal component is aₙ = b cos60 = b/2.

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