Question

A car is driving along a level and unbanked circular track of diameter d=0.94km at a constant speed of v=22.2m/s. What is the acceleration of the car?

1) 0 m/s²
2) 2.5 m/s²
3) 5 m/s²
4) 10 m/s²

Answer 1

The acceleration of a car on a circular track is found using the centripetal acceleration formula. The calculated value is approximately 1.05 m/s², which does not match the exact options given, suggesting a potential misprint in the question.

Step-by-step explanation:

The question pertains to the concept of centripetal acceleration in circular motion which is a common topic in high school physics. To find the acceleration of a car moving along a circular track, we can use the formula for centripetal acceleration, ac = v2 / r, where v is the linear speed and r is the radius of the circle.

First, we need to convert the diameter d = 0.94 km to the radius in meters, r = d/2 = 0.94 km / 2 = 0.47 km = 470 m. Next, we use the given speed v = 22.2 m/s and apply the centripetal acceleration formula: ac = (22.2 m/s)2 / 470 m = 493.84 m2/s2 / 470 m ≈ 1.05 m/s2.

This value is not exactly one of the provided options, but it is closest to option 2, therefore, the acceleration of the car is approximately 1.05 m/s2, which would be rounded to 1.0 m/s2 if it were an available choice. Since it is not, and assuming that the provided options are correct and exhaustive, there may be a misprint in the question. It is essential to notify the student to check for any possible errors or clarifications in the question.