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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
17=2t%5E2-3t Start with the given equation


17=2t%5E2-3t Plug in s=17


0=2t%5E2-3t-17 Subtract 17 from both sides.

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


Starting with the general quadratic

at%5E2%2Bbt%2Bc=0

the general solution using the quadratic equation is:

t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29



So lets solve 0=2%2At%5E2-3%2At-17 ( notice a=2, b=-3, and c=-17)




t+=+%28--3+%2B-+sqrt%28+%28-3%29%5E2-4%2A2%2A-17+%29%29%2F%282%2A2%29 Plug in a=2, b=-3, and c=-17



t+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%2A2%2A-17+%29%29%2F%282%2A2%29 Negate -3 to get 3



t+=+%283+%2B-+sqrt%28+9-4%2A2%2A-17+%29%29%2F%282%2A2%29 Square -3 to get 9 (note: remember when you square -3, you must square the negative as well. This is because %28-3%29%5E2=-3%2A-3=9.)



t+=+%283+%2B-+sqrt%28+9%2B136+%29%29%2F%282%2A2%29 Multiply -4%2A-17%2A2 to get 136



t+=+%283+%2B-+sqrt%28+145+%29%29%2F%282%2A2%29 Combine like terms in the radicand (everything under the square root)




t+=+%283+%2B-+sqrt%28145%29%29%2F4 Multiply 2 and 2 to get 4

So now the expression breaks down into two parts

t+=+%283+%2B+sqrt%28145%29%29%2F4 or t+=+%283+-+sqrt%28145%29%29%2F4


So these expressions approximate to

t=3.76039864469807 or t=-2.26039864469807


So our possible solutions are:

t=3.76039864469807 or t=-2.26039864469807



However, since a negative time doesn't make sense, our only solution is t=3.76039864469807


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