Four racecars are driving at constant speeds around a circular racetrack. The data table gives the speed of each car and each car’s distance from the center of the track at one instant.

Car Speed (m/s) Position (m)
A 40 20
B 40 25
C 50 20
D 50 25
Rank the cars’ accelerations from largest to smallest. To rank items as equivalent, overlap them.

Well, considering that the cars are already driving at a constant speed, their accelerations would all be zero. So, the ranking would look like this:

1. A, B, C, D (all with zero acceleration)

To determine the cars' accelerations, we need to calculate the change in speed over time. However, since there is no time data given, we cannot directly calculate the accelerations.

Nevertheless, we can analyze the situation based on the given information.

Car A and Car B both have the same speed and different positions, meaning they are not accelerating but moving at a constant speed.

Similarly, Car C and Car D both have the same speed and different positions, indicating that they are also moving at a constant speed.

Therefore, all four cars have the same acceleration, which is zero.

As a result, the cars' accelerations are all equivalent, so we can rank them as overlap.

Ranking:
A = B = C = D

To rank the cars' accelerations, we first need to determine the acceleration of each car. The acceleration of an object can be calculated using the formula:

Acceleration = (change in velocity) / (change in time)

Here, we need to find the change in velocity for each car. The change in velocity can be determined by subtracting the initial velocity from the final velocity. However, the data only gives us the speed (magnitude of velocity) of each car and not the final and initial velocities individually.

To find the change in velocity, we need to consider the direction of each car's motion. Since the cars are moving in a circular racetrack, their velocities are changing direction continuously. Therefore, we can calculate their accelerations using the centripetal acceleration formula:

Acceleration = (velocity^2) / (radius)

In this case, the radius would be the distance from the center of the track. Let's calculate the acceleration for each car using this formula:

Car A:
Acceleration (A) = (40^2) / 20 = 80 m/s^2

Car B:
Acceleration (B) = (40^2) / 25 = 64 m/s^2

Car C:
Acceleration (C) = (50^2) / 20 = 125 m/s^2

Car D:
Acceleration (D) = (50^2) / 25 = 100 m/s^2

Now, let's rank the cars' accelerations from largest to smallest:

Acceleration (C) = 125 m/s^2
Acceleration (D) = 100 m/s^2
Acceleration (A) = 80 m/s^2
Acceleration (B) = 64 m/s^2

So, the cars' accelerations, ranked from largest to smallest, are C > D > A > B.

Ac = v^2/R

for A it is 1600/20 = 80 m/s^2
for B it is 1600/25 = 64 m/s^2
etc