The velocity equation is:
[tex]v(x) = 108 - 24x[/tex]
Such that:
[tex]v(0) = 108 ft/s\\v(2) = 60ft/s\\[/tex]
And the velocity is zero for x = 4.5
How to find the velocity equation?
We know that the position equation is:
[tex]f(x) = 108*x - 12*x^2[/tex]
To get the velocity, we need to differentiate with respect to x, so we get:
[tex]v(x) = \frac{df(x)}{dx} = 108 - 2*12*x = 108 - 24*x[/tex]
Now we want to get the velocity for x = 0 and x = 2, we will get:
[tex]v(0) = 108 - 24*0 = 108\\\\v(2) = 108 - 24*2 = 60[/tex]
Then, when x = 0, the velocity is 108 ft/s, when x = 2 the velocity is 60 ft/2.
Finally, we need to solve:
[tex]v(x) = 108 - 24*x = 0\\\\x = 108/24 = 4.5[/tex]
The velocity is zero when x = 4.5
If you want to learn more about velocity:
https://brainly.com/question/4931057
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