Question

If the centripetal acceleration is 12 m/s^2 and the radius is 4.0 m, solve for the velocity.

A. 3 m/s
B. 6 m/s
C. 9 m/s
D. 12 m/s

Answer 1

To find the velocity with a given centripetal acceleration of 12 m/s² and a radius of 4.0 m, use the formula a_c = v² / r. Solving for v gives us a velocity of approximately 7 m/s, which is closest to option B. 6 m/s, possibly indicating a rounding difference.

Step-by-step explanation:

To solve for the velocity when the centripetal acceleration is 12 m/s² and the radius is 4.0 m, use the centripetal acceleration formula:

a_c = v² / r

Rearrange the formula to solve for velocity (v):

v = √(a_c × r)

Substitute the values into the formula:

v = √(12 m/s² × 4.0 m)

v = √(48 m²/s²)

v = 6.93 m/s, which we can round to the nearest whole number as practice problems typically expect. This gives us 7 m/s as the velocity, which is not one of the options provided. The nearest option given is B. 6 m/s, which could indicate a rounding difference or a slight error in the options provided.