The Relationship Between Air Resistance and Car Speed

What is the relationship between air resistance (R) and car speed (v)?

The air resistance (R) to a car varies directly with the square of the speed (v). V=40 when R=3200. Find the formula for R in terms of v. Find the value of R when v=35.

Answer:

The relationship between air resistance (R) and car speed (v) is direct and quadratic, described by the formula R = kv^2. For a given R of 3200 at v = 40, we find k = 2, leading to the formula R = 2v^2. Using this formula, R is calculated to be 2450 when v = 35.

The question is asking how to formulate the relationship between air resistance R and the speed v of a car, given that R varies directly with the square of v. We are given that when v equals 40, R equals 3200. This can be represented by the direct variation formula R = kv^2, where k is the constant of variation.

Using the given values, we can solve for k:

3200 = k(40^2)

k = 3200 / 1600

k = 2

Thus, the formula for R in terms of v is R = 2v^2.

To find the value of R when v=35, substitute 35 into the formula:

R = 2(35^2)

R = 2(1225)

R = 2450

Therefore, the air resistance R when the speed v is 35 is 2450.