The distance that an object will fall in (t) seconds varies directly with the square of (t). An object falls 5 feet in 1 second. How long will it take to fall 125 feet?

Question

The distance that an object will fall in (t) seconds varies directly with the square of (t).  An object falls 5 feet in 1 second.  How long will it take to fall 125 feet?

anonymous · Answer

If a term varies directly with t, velocity is an example, 
$$ v \propto t $$
we can say that
$$  \frac{v_!}{v_2} \propto  \frac{t_!}{t_2} $$
and set up the proportional equation
$$ \frac{v_!}{v_2} = \frac{t_!}{t_2} $$

Since x varies with t squared

$$ x \propto t_2$$

....

anonymous · Answer

~~~
$$ x \propto t^2 $$

anonymous · Answer

How might you set up a proportional equation to solve for an unknown value of t?

anonymous · Answer

5/125=1/t^2
=> t=5s

anonymous · Answer

$$(125 feet)\frac{ 1second }{ 5 feet}=25 seconds$$
We must set up a proportion so that the object takes 1 second to fall 5 feet. 
Feet would cancel out leaving seconds.

I could be incorrect, please let me know if I am wrong.

anonymous · Answer

@anthonykanow

It's proportional to t^2, so should look like 

$$ \frac{x_1}{x_2} = \frac{t_1^2}{t_2^2} $$
$$ 125 ft \frac {1s^2}{5ft} =25s^2 $$
$$t_2^2 = 25 s^2$$

So the time would be the square root of 25