Answer :
The acceleration if we double the speed is 27 m/s².
How to find the acceleration if we double the speed?
A centripetal acceleration, or acceleration toward the center of the circle, results from moving in a constant circular motion.
a = v²/r is the formula for calculating an object's circular motion acceleration.
Since the radius never changes, let's set it at 5 m. Using a = 3 m/s² and r = 3m to solve for the velocity, we get the following results:
Were, 3 = v²/3
simplifying the equation, we get
⇒ 9 = v²
⇒ 3 = v
When the circular path has a radius of 3 m and an acceleration of
3 m/s², the velocity is 3 m/s.
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
If you triple your speed, the acceleration is 27 m/s².
This makes sense because an is precisely proportional to v², which means that if your speed is tripled, your acceleration will increase by a factor of 3², or nine times.
a = 3 [tex]*[/tex] 9 = 27 m/s²
As a side note, doubling your speed would improve the acceleration by a factor of 2² - a 4 times increase.
To learn more about acceleration refer to:
https://brainly.com/question/605631
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