An object travels in a circular path at speed vand experiences a centripetal acceleration ac. What will be the object's new centripetal acceleration, if its speed is increased to 2.0V?

Option B. 4a꜀

Explanation:

From the question given above, the following data were obtained:

Initial speed (v₁) = v

Initial acceleration (a₁) = a꜀

New speed (v₂) = 2v

New acceleration (a₂) =?

Centripetal acceleration is given by the following equation:

a = v²/ r

Next, we shall make r the subject.

a = v²/ r

Cross multiply

a × r = v²

Divide both side by a

r = v² / a

NOTE: We assume the radius (r) to be constant.

v₁² / a₁ = v₂² / a₂

Thus, we shall determine the new acceleration as follow:

Initial speed (v₁) = v

Initial acceleration (a₁) = a꜀

New speed (v₂) = 2v

New acceleration (a₂) =?

v₁² / a₁ = v₂² / a₂

v² / a꜀ = (2v)² / a₂

v² / a꜀ = 4v² / a₂

Cross multiply

v² × a₂ = a꜀ × 4v²

Divide both side by v²

a₂ = a꜀ × 4v² / v²

a₂ = a꜀ × 4

a₂ = 4a꜀

Therefore, the new centripetal acceleration of the object is 4a꜀

4.0 · ac

Explanation:

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