Answer:
27 m/s²
Explanation:
Traveling in uniform circular motion will cause a centripetal acceleration, an acceleration towards the center of the circle.
The acceleration of an object in circular motion is defined as a = v²/r.
Let's set the radius to be 5 m, since it is always unchanging. Solving for the velocity using a = 3 m/s² and r = 3 m gives us:
The velocity is 3 m/s when the acceleration is 3 m/s² and the radius of the circular path is 3 m.
Now let's triple the velocity: 3 m/s → 9 m/s.
Let's solve for the acceleration using v = 9 m/s and r = 3 m.
The acceleration is 27 m/s² if you triple your speed.
This makes sense because a is directly proportional to v², meaning that if you triple your speed, you increase the acceleration a by a factor of 3², which is a 9 times increase.
As a sidenote, doubling your speed would increase the acceleration by a factor of 2² - a 4 times increase.
Answer:
27 m/s²
Explanation:
Traveling in uniform circular motion will cause a centripetal acceleration, an acceleration towards the center of the circle.
The acceleration of an object in circular motion is defined as a = v²/r.
Let's set the radius to be 5 m, since it is always unchanging. Solving for the velocity using a = 3 m/s² and r = 3 m gives us:
3 = v²/3
9 = v²
3 = v
The velocity is 3 m/s when the acceleration is 3 m/s² and the radius of the circular path is 3 m.
Now let's triple the velocity: 3 m/s → 9 m/s.
Let's solve for the acceleration using v = 9 m/s and r = 3 m.
a = (9)²/3
a = 81/3
a = 27
The acceleration is 27 m/s² if you triple your speed.
This makes sense because a is directly proportional to v², meaning that if you triple your speed, you increase the acceleration a by a factor of 3², which is a 9 times increase.
a = 3 * 9 = 27 m/s²
As a sidenote, doubling your speed would increase the acceleration by a factor of 2² - a 4 times increase.
