A truck drives with a constant linear speed v_iv i v, start subscript, i, end subscript down a road with two curves. The first curve has a radius RRR and the second curve has a radius 3R3R3, R. How does the magnitude of the truck's centripetal acceleration change after the radius increases? Choose 1 Choose 1 (Choice A) A Increases by factor of 333 (Choice B) B Decreases by factor of 999 (Choice C) C Decreases by factor of 333 (Choice D) D No change

(C) Decreases by factor of 3

Explanation:

Centripetal acceleration is given by

where v is the linear velocity and r is the radius of the curve.

Let the centripetal acceleration on the curve of radius R be .

Then

Let the centripetal acceleration on the curve of radius 3R be .

Then

Here, we see that the acceleration decreases by a factor of 3.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .