The resistance to the motion of a vehicle is partly constant and partly varies as the square of it's speed.At 30km/h the resistance is 496N,and 50km/h it is 656N.
Find the resistance at 60km/h.
R = a + v^2 b
496 = a + 900 b
856 = a + 2500 b
-------------------------subtract
-360 = -1600 b
b = 0.225
a = -2500 (0.225) +856 = 294
so
R = 294 + 0.225 v^2
at v = 60
R= 294 +0.225 (3600) = 1104 Newtons
To find the resistance at 60 km/h, we need to first determine the constant resistance (C) and the resistance that varies as the square of the speed (k).
Let's denote the constant resistance as C and the resistance that varies as the square of the speed as k.
We are given the following information:
At 30 km/h, the resistance is 496 N.
At 50 km/h, the resistance is 656 N.
We can set up two equations to solve for C and k:
Equation 1: C + k(30)^2 = 496
Equation 2: C + k(50)^2 = 656
We need to solve these equations simultaneously.
Step 1: Solve Equation 1 for C.
C + k(900) = 496
C = 496 - 900k
Step 2: Substitute the value of C from Step 1 into Equation 2.
496 - 900k + k(2500) = 656
496 - 900k + 2500k = 656
1600k = 656 - 496
1600k = 160
k = 160 / 1600
k = 0.1
Step 3: Substitute the value of k into Equation 1 to find C.
C + (0.1)(900) = 496
C + 90 = 496
C = 496 - 90
C = 406
Step 4: Substitute the values of C and k into the equation for the resistance at 60 km/h.
Resistance at 60 km/h = C + k(60)^2
Resistance at 60 km/h = 406 + (0.1)(3600)
Resistance at 60 km/h = 406 + 360
Resistance at 60 km/h = 766 N
Therefore, the resistance at 60 km/h is 766 N.
To find the resistance at 60 km/h, we need to determine the constant and variable components of the resistance and then use the given information to solve for the unknown resistance value.
Let's assume that the constant resistance is represented by R1 and the variable resistance is represented by R2. We are given two conditions:
At 30 km/h: Resistance (R) = 496 N
At 50 km/h: Resistance (R) = 656 N
From the given information, we can set up the following equations:
Equation 1: R = R1 + R2 = 496 N
Equation 2: R = R1 + (50^2)R2 = 656 N
To find R1 and R2, we can solve these equations simultaneously.
Subtracting Equation 1 from Equation 2, we get:
(50^2)R2 - R2 = 656 - 496
(2500 - 1)R2 = 160
2499R2 = 160
Now, we can solve for R2:
R2 = 160 / 2499
Substituting the value of R2 back into Equation 1, we can find R1:
496 = R1 + (30^2)(160 / 2499)
496 = R1 + 28800 / 2499
496 = R1 + 11.5254
R1 = 496 - 11.5254
R1 = 484.4746
Therefore, the constant resistance R1 is approximately 484.47 N, and the variable resistance R2 is approximately 0.064 N/km^2.
Now, to find the resistance at 60 km/h, we can use the formula:
Resistance (R) = R1 + (60^2)R2
Plugging in the values we found:
R = 484.47 + (60^2)(0.064)
R = 484.47 + 230.4
R ≈ 714.87 N
Therefore, the resistance at 60 km/h is approximately 714.87 N.