Car A travels with speed v around curve number one, which has a radius r. Car B

travels with speed 2v around curve number two, which has a radius 2r. What is the ratio
of the two accelerations A/B?
A) 2
B) 4
C) 1/2
D) 1/4
E) 1

centripetal acceleration= v^2/r=s^2/r

car A: s^2/r
1/1=1

car B: s^2/r
2s^2/2r
4s/2r
=2

Car A/B= 1/2

To find the ratio of the two accelerations A/B, we need to use the formula for centripetal acceleration:

a = v^2 / r

For car A:

Acceleration of A = v^2 / r

For car B:

Acceleration of B = (2v)^2 / (2r) = 4v^2 / 2r = 2v^2 / r

Now let's find the ratio A/B:

Ratio of A/B = (v^2 / r) / (2v^2 / r)

Cancel out the common terms:

Ratio of A/B = (v^2 * r) / (2v^2 * r)

Simplify:

Ratio of A/B = 1 / 2

Therefore, the ratio of the two accelerations A/B is:

C) 1/2