You are taking a turn at 23.0 m/s on a ramp of radius 39.0 m. What is your acceleration?

Question

BlackTom AI · Accepted Answer

Begin by identifying the physics concept: for an object moving in a circle, the acceleration is centripetal and given by a = v^2 / r.
Option 1: 13.6 m/s2. This matches the calculation a = (23.0 m/s)^2 / (39.0 m) = 529 / 39 ≈ 13.56, which rounds to 13.6 m/s2.
Option 2: 66.1 m/s2. This would require a much larger result; it could come from squaring a far larger velocity or using a smaller radius, but with the given v and r, 66.1 is not supported by the formula.
Option 3: 0.59 m/s2. This is roughly an order of magnitude smaller than the correct centripetal value, suggesting either an incorrect radius or a misplacement of v in the numerator/denominator.
Option 4: 1.70 m/s2. Similarly, this is also far from the correct result and would imply an incorrect combination of v and r in the a = v^2 / r expression.
To confirm, substitute the numbers directly into a = v^2 / r: a = (23.0)^2 / 39.0 ≈ 529 / 39 ≈ 13.56 m/s2, which is consistent with Option 1. The other options do not satisfy the centripetal acceleration formula with the given speed and radius.

You are taking a turn at 23.0 m/s on a ramp of radius 39.0 m. What is your acceleration?单项选择题

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