A race car goes around a circular, level track with a diameter of 1.00 km at a constant speed of 90.0 km/h. What is the car's centripetal acceleration in m/s^2?
To find the car's centripetal acceleration, we can use the formula:
a = v^2 / r
Where "a" is the centripetal acceleration, "v" is the velocity, and "r" is the radius of the circular track.
Given that the diameter of the circular track is 1.00 km, the radius will be half of the diameter, which is:
r = 1.00 km / 2 = 0.50 km
We need to convert the radius and velocity to meters, since the unit for acceleration is meters per second squared (m/s^2).
1 km = 1000 m, so the radius in meters will be:
r = 0.50 km * 1000 m/km = 500 m
The velocity of the car is given as 90.0 km/h. Converting this to meters per second:
90.0 km/h * 1000 m/km * 1 h/3600 s = 25 m/s
Now we can substitute the values into the formula:
a = (25 m/s)^2 / 500 m
a = 625 m^2/s^2 / 500 m
a = 1.25 m/s^2
Therefore, the centripetal acceleration of the race car is 1.25 m/s^2.
To find the car's centripetal acceleration, we need to use the formula for centripetal acceleration:
a = v^2 / r
Where:
a = centripetal acceleration
v = velocity of the car
r = radius of the circular track
First, let's convert the velocity from km/h to m/s:
1 km = 1000 m
1 h = 3600 s
So, 90.0 km/h = 90.0 * 1000 / 3600 m/s = 25.0 m/s
Next, we need to find the radius of the circular track. The diameter is given as 1.00 km, so the radius is half of that:
r = 1.00 km / 2 = 0.50 km = 0.50 * 1000 m = 500 m
Now, we can substitute the values into the formula to find the centripetal acceleration:
a = (25.0 m/s)^2 / 500 m
a = 625.0 m^2/s^2 / 500 m
a = 1.25 m/s^2
Therefore, the car's centripetal acceleration is 1.25 m/s^2.
20
Ac = v^2/R
R = 500 meters
v = 90 km/h * 1000 meters/km * 1 hr/3600 s