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