Question

The data in the table listed below relates the distance a ball travels down a ramp to the time that has passed since it was released.
Find a variation equation that fits the data.
Time, t(sec)| 0,1,2,3,4,5
Distance, d(in)| 0, 0.4, 1.6, 3.6, 6.4, 10.0

Answer 1

The x-values (Time) are increasing by 1.
Take the differences in the y-values (Distance):
0.4, 1.2, 2.0, 2.8, 3.6
Since the y-values are NOT increasing by the same amount each time the variation is NOT linear. Take the differences one more time:
0.8, 0.8, 0.8, 0.8.
The second differences are constant and therefore this is a quadratic variation.

Answer 2

Soooo could you give me an example of what you would write for an variation equation?

Answer 3

@aum

Answer 4

Try y = ax^2
when x = 1, y = a = 0.4
so a = 0.4
y = 0.4x^2
x = 1, y = 0.4
x = 2, y = 0.4 * 4 = 1.6
x = 3, y = 0.4 * 9 = 3.6
....

Answer 5

okay. that makes sense. so whats the equation you would create to describe this?

Answer 6

Distance d = 0.4 * t^2

Answer 7

You put t = 0, 1, 2, 3, 4,5 into the equation d = 0.4 * t^2 and you will get the d values given in the table.

Answer 8

gotcha so your answer is d= 0.4*t^d"?

Answer 9

\[\Large d = 0.4t^2\]