SOLUTION: Hello I hope someone can help me. Here is the question: THe position of an object moving in a straight line is given by s= 2t^2 - 3t, where s is in meters and t is the time in sec

Question 132818: Hello
I hope someone can help me. Here is the question: THe position of an object moving in a straight line is given by s= 2t^2 - 3t, where s is in meters and t is the time in seconds the object has been in motion. How long (to the nearest tenth) wiil it take the object to move 17 meters?
I am so lost! SO far what I have gotten from this is:
17= 2t^2 - 3t
2t^2 - 3t - 17= 0 But now what do I do? Please help-THank you!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Plug in

Subtract 17 from both sides.

Let's use the quadratic formula to solve for t:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=2, b=-3, and c=-17

Negate -3 to get 3

Square -3 to get 9 (note: remember when you square -3, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Multiply 2 and 2 to get 4

So now the expression breaks down into two parts

or

So these expressions approximate to

or

So our possible solutions are:

or

However, since a negative time doesn't make sense, our only solution is

So it takes about 3.76 seconds for the object to move 17 meters

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