Question

An object traveling at constant speed v in a circle of radius R has an acceleration a = 5 m/s2. If both Rand v are doubled, what is the new acceleration?

40 m/s^2
10 m/s^2
5 m/s^2
2.5 m/s^2

Answer 1

When the radius and speed of an object moving in a circular path are both doubled, its centripetal acceleration would also double. Thus, if the original acceleration is 5 m/s², the new acceleration will be 10 m/s².

Step-by-step explanation:

The original acceleration of an object moving at a constant speed in a circle with radius R and speed v is given by the centripetal acceleration formula a = v²/R. When both the radius R and the speed v are doubled, the new radius is 2R and the new speed is 2v. Substituting these into the formula, the new acceleration a' is (2v)² / (2R) = 4v² / 2R = 2v² / R = 2a, where a is the original acceleration. Therefore, if the original acceleration a is 5 m/s², the new acceleration a' would be 10 m/s².