Question

If an object moves along the y-axis (marked in feet) so that it’s position at time X (in seconds) is given by f(x) = 108x -12x^2 , find the following:

Answer 1

The velocity equation is:

$v(x) = 108 - 24x$

Such that:

$v(0) = 108 ft/s\\v(2) = 60ft/s$

And the velocity is zero for x = 4.5

How to find the velocity equation?

We know that the position equation is:

$f(x) = 108*x - 12*x^2$

To get the velocity, we need to differentiate with respect to x, so we get:

$v(x) = \frac{df(x)}{dx} = 108 - 2*12*x = 108 - 24*x$

Now we want to get the velocity for x = 0 and x = 2, we will get:

$v(0) = 108 - 24*0 = 108\\\\v(2) = 108 - 24*2 = 60$

Then, when x = 0, the velocity is 108 ft/s, when x = 2 the velocity is 60 ft/2.

Finally, we need to solve:

$v(x) = 108 - 24*x = 0\\\\x = 108/24 = 4.5$

The velocity is zero when x = 4.5

If you want to learn more about velocity:

brainly.com/question/4931057

#SPJ1