A resistance R newtons to the motion of a car varies directly as the square of the speed S.
(A)write the equation conneting R and S
(B) given that R=25N and S=4.find S given that R=36
(A) R = k S^2
(B) 25 = k * 16 ... k = 25/16
S = √(R / k) = √[36 / (25/16)] = 6 / (5/4) = 24/5
(A) The equation connecting R and S can be written as R = kS^2, where k represents the constant of proportionality.
(B) To find S given that R = 36, we can use the formula R = kS^2 with the given value of R.
36 = kS^2
To solve for S, we need to find the value of k. We can do this by using the given information that R = 25 when S = 4.
25 = k(4)^2
25 = 16k
k = 25/16 = 1.5625
Now, substituting the value of k back into the equation:
36 = 1.5625S^2
Divide both sides by 1.5625:
23.04 = S^2
Taking the square root of both sides, we find:
S ≈ 4.8
Therefore, when R = 36 N, S is approximately equal to 4.8.
(A) According to the given information, the resistance R is directly proportional to the square of the speed S. This can be represented by the equation:
R = k * S^2
where k is the constant of proportionality.
(B) Using the equation from part (A), and the given values R = 25 N and S = 4, we can find the value of k:
25 = k * 4^2
25 = k * 16
k = 25 / 16
Now, we can use the value of k to find S when R = 36:
36 = (25 / 16) * S^2
36 * 16 = 25 * S^2
576 = 25 * S^2
S^2 = 576 / 25
S^2 = 23.04
To find S, we take the square root of both sides:
S = √(23.04)
S ≈ 4.8
Therefore, given that R = 36 N, the speed S is approximately 4.8.
To solve this problem, we can use the given information that the resistance R varies directly as the square of the speed S. This means that we have a direct variation relationship between R and S which can be represented by the equation:
(A) R = k * S^2
In this equation, k is the constant of variation. We need to find the value of k to complete the equation.
To do this, we can use the given values of R and S and substitute them into the equation.
(B) Given: R = 25 N and S = 4
Substituting these values into equation (A):
25 = k * (4)^2
25 = k * 16
25/16 = k
So, the value of k is 25/16.
Now, we can use this value of k to find S when R = 36.
Substituting R = 36 into equation (A) with k = 25/16:
36 = (25/16) * S^2
To find S, we need to isolate it. Divide both sides by (25/16):
36 / (25/16) = S^2
(36 * 16) / 25 = S^2
(576) / 25 = S^2
Now, take the square root of both sides to isolate S:
√[(576) / 25] = S
(√576) / (√25) = S
(24) / (5) = S
So, when R = 36 N, S is approximately equal to 4.8.