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A race car moving along a circular track has a centripetal acceleration of 15.4^2. If the car has a tangential speed of 30 what is the distance between the car and the center of the track?

Respuesta :

Answer:

58.44m

Step-by-step explanation:

Centripetal acceleration in a circular path is defined as follows:

[tex]a_{c}=\frac{v^2}{r}[/tex]

Where [tex]a_{c}[/tex] is the centripetal acceleration,  [tex]v[/tex] is the tangential speed, and  [tex]r[/tex] is the radius of the circle.

Since we need to know the distance between the car and the center of the track, we are looking for the radius of the circular track  [tex]r[/tex], so we clear for it in the last equation:

[tex]r=\frac{v^2}{a_{c}}[/tex]

And since we have the following information:

centripetal acceleration: [tex]a_{c}=15.4m/s^2[/tex]

tangential speed: [tex]v=30m/s[/tex]

We substitute these values in the equation to find the radius:

[tex]r=\frac{v^2}{a_{c}}=\frac{(30m/s)^2}{15.4m/s^2}=\frac{900m^2/s^2}{15.4m/s^2}=58.44m[/tex]

The distance between the car and the center of the track is 58.44m

Lanuel

The distance between the car and the center of the track is 58.44 meters.

Given the following data:

  • Centripetal acceleration = 15.4 [tex]m/s^2[/tex]
  • Tangential speed = 30 m/s.

To calculate the distance between the car and the center of the track:

How to calculate centripetal acceleration.

Mathematically, the centripetal acceleration of an object is given by this formula:

[tex]A_c = \frac{V^2}{r}[/tex]

Where:

  • [tex]A_c[/tex] is the centripetal acceleration.
  • r is the distance (radius) from a circular track.
  • V is the velocity of an object.

Making r the subject of formula, we have:

[tex]r=\frac{V^2}{A_c}[/tex]

Substituting the given parameters into the formula, we have;

[tex]r=\frac{30^2}{15.4}\\\\r=\frac{900}{15.4}[/tex]

r = 58.44 meters.

Read more on centripetal acceleration here: https://brainly.com/question/2788500

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