the velocity of an object in liquid can be described by the equation: v = 20 - t - t^2 where v is the velocity in meters per second and t is time in seconds.

You can also rewrite this as t² + t - 20 = 0

 

This factorizes nicely:

(t + 5)(t - 4) = 0

 

Since we can't have a negative value for time in this problem the only valid solution is t = 4 seconds, just as Anonymous found.

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$${\mathtt{v}} = {\mathtt{20}}{\mathtt{\,-\,}}{\mathtt{t}}{\mathtt{\,-\,}}{{\mathtt{t}}}^{{\mathtt{2}}}$$

Set V equal to 0

$${\mathtt{0}} = {\mathtt{20}}{\mathtt{\,-\,}}{\mathtt{t}}{\mathtt{\,-\,}}{{\mathtt{t}}}^{{\mathtt{2}}}$$

Subtract 20 from zero

$$-{\mathtt{20}} = {\mathtt{\,-\,}}{\mathtt{t}}{\mathtt{\,-\,}}{{\mathtt{t}}}^{{\mathtt{2}}}$$

Flip both sides so they are both positive

$${\mathtt{t}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{t}}}^{{\mathtt{2}}} = {\mathtt{20}}$$

There is proabably a more proper way to do it, but i just cycled through squares of low numbers untill i got the answer >.> It's t=4

$${\mathtt{4}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{4}}}^{{\mathtt{2}}} = {\mathtt{20}}$$

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