A curving freeway exit has a radius of 50.5m m and a posted speed limit of 35 mi/h \rm mi/h.
What is the radical acceleration (in m/s^2) if you take the exit as posted speed
express answer to two significant figures and appropriate units.
Thanks for any help.
To find the radial acceleration, we need to use the formula:
radial acceleration = (speed^2) / radius
First, let's convert the speed limit from miles per hour to meters per second.
1 mile = 1609.34 meters (conversion factor)
35 miles = 35 * 1609.34 meters
35 miles = 56352.9 meters
1 hour = 3600 seconds (conversion factor)
35 miles per hour = 56352.9 meters per 3600 seconds
35 miles per hour = 15.709 meters per second (approximately)
Now we can substitute the converted speed and the given radius into the formula to calculate the radial acceleration:
radial acceleration = (15.709 m/s)^2 / 50.5 m
Simplifying the equation:
radial acceleration = 246.958881 m^2/s^2 / 50.5 m
radial acceleration = 4.881274 m/s^2 (approximately)
Therefore, the radial acceleration, when taking the exit at the posted speed limit, is approximately 4.88 m/s^2.