The resistance ( R ) to a motion of a car is partly constant and partly varies as the square of the speed ( V ) When the car is moving at ( 20KM/H ) The resistance is (720 OHMS ) and at ( 60KM/H ) the resistance is 232 ohms fine an expression for ( R ) of ( V ) the resistance at 40km/h
R = c + kV^2
when V = 20, R = 720
c + 400k = 720
when V = 60, R = 232
c + 3600k = 232
subtract the two equations ...
3200k = -488
k = -61/400
back in first equation:
c + 400(-61/400) = 720
c = 781
R = 781 - (61/400) V^2
Now that we have the equation, you can finish your question.
SIR
SAMUEL
Why did the car go to the comedy club? Because it wanted to resist a moving performance!
Based on the given information, we can determine that the resistance (R) of the car depends on both a constant value and the square of the speed (V). Let's break it down step by step:
When the car is moving at 20 km/h, the resistance is 720 ohms.
When the car is moving at 60 km/h, the resistance is 232 ohms.
To find the expression for R in terms of V, we can use the given information to set up a system of equations:
Equation 1: R = k + aV^2 (where k is the constant resistance and a is a coefficient)
Equation 2: 720 = k + a(20)^2
Equation 3: 232 = k + a(60)^2
Now, let's solve these equations to determine the values of k and a:
From Equation 2: 720 = k + 400a
From Equation 3: 232 = k + 3600a
Subtracting Equation 2 from Equation 3, we get:
232 - 720 = k + 3600a - (k + 400a)
-488 = 3200a
a = -488/3200
a = -0.1525
Now, substitute the value of a back into Equation 2 to solve for k:
720 = k + 400(-0.1525)
720 = k - 61
k = 781
So, the expression for R in terms of V, the resistance at 40 km/h, is:
R(V) = 781 - 0.1525V^2
Just remember, resistance might try to slow the car down, but it can't resist the power of laughter!
To find an expression for the resistance (R) as a function of speed (V), we can use the information given about the resistance at different speeds.
Let's consider the constant part of the resistance as K, and the part that varies with the square of the speed as (V^2).
We are given two data points:
1. When the car is moving at 20 km/h, the resistance is 720 ohms.
2. When the car is moving at 60 km/h, the resistance is 232 ohms.
Using these data points, we can set up the following equations:
Equation 1: R = K + V^2
Substituting the values from the first data point:
720 = K + (20^2) --> 720 = K + 400 --> K = 720 - 400 --> K = 320
Now we have the constant part of the resistance, K, which is 320 ohms.
Equation 2: R = K + V^2
Substituting the values from the second data point:
232 = 320 + (60^2) --> 232 = 320 + 3600 --> 232 - 320 = 3600 --> 88 = 3600
Now we can substitute the value of K into Equation 2:
R = 320 + V^2
To find the resistance at 40 km/h, we can simply substitute V = 40 into the expression:
R = 320 + (40^2) --> R = 320 + 1600 --> R = 1920 ohms
Therefore, the expression for the resistance (R) as a function of speed (V) is:
R = 320 + V^2
And the resistance at 40 km/h is 1920 ohms.