Question

2. An object is experiencing an acceleration of 12 m/s² while traveling in a circle at a velocity of 3.1 m/s.

What is the radius of its motion?

Answer 1

0.8 meters

Step-by-step explanation:

When an object is moving at a constant velocity in a circular motion, the only acceleration acting on it is the centripetal acceleration which is directd toward the center of the circle

The formula for centripetal acceleration is

`a_c = (v^2)/(r) \dots[1]`

where

`\text {$a_c$ is the centripetal acceleration}\\\\\text {$v$ is the velocity}\\\\\text{$r$ is the radius of the circular path}\\\\`

Given

`a_c = 12\;m/s^2\\v = 3.1\;m/s`

we can plug in these values into the formula to determine r

`12 = (3.1^2)/(r)`

`r = (3.1^2)/(12) = (9.61)/(12) = 0.80 \;m`