Question 316415: The kinetic energy, K, of a moving particle acted on by various forces depends quadratically on the velocity, x, of the particle. The particle's energy is 210 ergs when its velocity is 5 meters per second;860 ergs at 10 meters per second; and 2010 ergs at 15 meters per second. What is the quadratic function K(x) that fits this data?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The kinetic energy, K, of a moving particle acted on by various forces depends quadratically on the velocity, x, of the particle.
The particle's energy is 210 ergs when its velocity is 5 meters per second;
860 ergs at 10 meters per second; and
2010 ergs at 15 meters per second.
What is the quadratic function K(x) that fits this data?
:
Using the form K(x) = ax^2 + bx, find a & b by elimination
:
x=5; K(x)=210
5^2a + 5b = 210
25a + 5b = 210
Simplify, divide by 5
5a + b = 42
:
x=15; K(x)=2010
15^2a + 15b = 2010
225a + 15b = 2010
Simplify, divide by 5
45 + 3b = 402
:
Multiply the simplified version of the 1st equation by 3, subtract from above
45a + 3b = 402
15a + 3b = 126
--------------subtraction eliminates b, find a
30a = 276
a = 
a = 9.2
:
Find b using 5a + b= 42
5(9.2) + b = 42
b = 42 - 46
b = -4
:
The quadratic function: k(x) = 9.2x^2 - 4x
:
It fits exactly for x=5 and x=15
:
Check the fit using x=10;
k(x) = 9.2(10^2) - 4(10)
k(x) = 920 - 40
k(x) = 880 a slight difference, should be 860
:
Graphically; k(x) on the y axis
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