Question

Equals 9.81 m/s

Susan runs around a circular track with a circumference of 400 m. If she experiences a centripetal acceleration of
2.79 x 10 m/s, how long will it take to run one lap around the track? (Yes, you do have all the information you
need.)
that simulates gravity so that the astronauts do not export

Answer 1

To calculate the time it takes for Susan to run one lap around the track, we can use the formula T = 2πr/v, where T is the time, r is the radius of the track, and v is the linear velocity. The circumference of the track is 400 m, so the radius is half of that, which is 200 m. Given that the centripetal acceleration is 2.79 x 10 m/s, we can calculate the linear velocity using the formula v = √(ac * r). Substituting the values, we get v = √((2.79 x 10 m/s²) * 200 m) = 26.48 m/s. Finally, substituting the values into the formula for time, we have T = 2π(200 m) / (26.48 m/s) = 37.81 seconds.

Step-by-step explanation:

To calculate the time it takes for Susan to run one lap around the track, we can use the formula T = 2πr/v, where T is the time, r is the radius of the track, and v is the linear velocity.

The circumference of the track is 400 m, so the radius is half of that, which is 200 m.

Given that the centripetal acceleration is 2.79 x 10 m/s, we can calculate the linear velocity using the formula v = √(ac * r).

Substituting the values, we get v = √((2.79 x 10 m/s²) * 200 m) = 26.48 m/s.

Finally, substituting the values into the formula for time, we have T = 2π(200 m) / (26.48 m/s) = 37.81 seconds.