SOLUTION: The position of an object moving in a straight line is given by s=2tsquared-3t, where s is in meters and t is the time in seconds the object has been in motion. How long(to the nea

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The position of an object moving in a straight line is given by s=2tsquared-3t, where s is in meters and t is the time in seconds the object has been in motion. How long(to the nea      Log On


   

Question 186357: The position of an object moving in a straight line is given by s=2tsquared-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) will it take the object to move 6 meters?
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!

s=2tsquared-3t
s=2t^2-3t
.
Set 's' to 6 and solve for 't':
s=2t^2-3t
6=2t^2-3t
0=2t^2-3t-6
Since we can't factor, we must use the quadratic equation.
Doing so yields:
t = {2.6, -1.1}
We can toss out the negative solution leaving
t = 2.6 seconds
.
Details of quadratic follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-3x%2B-6+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-3%29%5E2-4%2A2%2A-6=57.

Discriminant d=57 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+57+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+57+%29%29%2F2%5C2+=+2.63745860881769
x%5B2%5D+=+%28-%28-3%29-sqrt%28+57+%29%29%2F2%5C2+=+-1.13745860881769

Quadratic expression 2x%5E2%2B-3x%2B-6 can be factored:
2x%5E2%2B-3x%2B-6+=+2%28x-2.63745860881769%29%2A%28x--1.13745860881769%29
Again, the answer is: 2.63745860881769, -1.13745860881769. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-3%2Ax%2B-6+%29