a stone is tied to the end of a string and is swung with a constant speed around a horizontal circle with a radius of 1.5m. if it makes two complete revolutions each second, what is the magnitude of its acceleration?

i know the answer, but i don't know how to get it. thank you!

acceleration= v^2/r

where v= 2PIr/.5sec

thank you sooo much! :)

To find the magnitude of the stone's acceleration, you can use the formula for centripetal acceleration, which is given by:

a = (v^2) / r

Where:
a is the magnitude of acceleration
v is the velocity
r is the radius of the circle

In this case, you are given that the stone makes two complete revolutions each second. Since one revolution is equal to the circumference of the circle, the velocity can be calculated using the formula:

v = 2πr / T

Where:
T is the time taken for one revolution (period of rotation)
r is the radius of the circle

In this case, T = 1 second and r = 1.5 m. Substituting these values into the formula, we get:

v = 2π(1.5) / 1
v ≈ 9.42 m/s

Now, substituting this value for v into the formula for centripetal acceleration:

a = (9.42^2) / 1.5
a ≈ 59.35 m/s^2

Therefore, the magnitude of the stone's acceleration is approximately 59.35 m/s^2.

To find the magnitude of the stone's acceleration, we can use the formula for centripetal acceleration. Centripetal acceleration (a) is defined as the rate of change of velocity (v) with respect to time (t) in circular motion.

The formula for centripetal acceleration is given by:
a = (v^2) / r

Where:
- a is the centripetal acceleration
- v is the velocity
- r is the radius of the circular path

From the given information, the stone makes two complete revolutions each second. This means it completes a full revolution (360 degrees or 2π radians) in half a second.

To determine the velocity (v) of the stone, you need to find the circumference of the circular path using the formula:
C = 2πr

Substituting the value of the radius (r = 1.5m) into the formula, we have:
C = 2π(1.5)
C ≈ 9.42m

Since the stone completes one full revolution (circumference) in half a second, the velocity is:
v = (C / t)
v = 9.42m / 0.5s
v = 18.84m/s

Now that we have the value of velocity (v = 18.84m/s) and radius (r = 1.5m), we can calculate the magnitude of the acceleration (a) using the formula:
a = (v^2) / r

Substituting the values into the formula, we have:
a = (18.84^2) / 1.5
a = 355.53m^2/s^2

Thus, the magnitude of the stone's acceleration is 355.53 m^2/s^2.