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 secoonds the object has been in motion. How long (to the

Algebra ->  Square-cubic-other-roots -> 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 secoonds the object has been in motion. How long (to the      Log On


   

Question 122844This question is from textbook college algebra
: 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 secoonds the object has been in motion. How long (to the nearest tenth) will it take the object to move 19 meters? This question is from textbook college algebra

Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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 secoonds the object has been in motion. How long (to the nearest tenth) will it take the object to move 19 meters?
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s(t) = 2t^2-3t
19 = 2t^2-3t
2t^2-3t-19=0
t = [3 +- sqrt(9-4*2*-19)]/4
t = [3 +- sqrt(161)]/4
t = [3 +- 12.6886]/4
Positive answer:
t = [3+12.6886]/4
t = 3.9221 seconds
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Cheers,
Stan H.


Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The problem can be solved by letting s (the distance in meters) = 19 and solving for t (the time in seconds):
s+=+2t%5E2-3t Substitute s = 19:
19+=+2t%5E2-3t Subtract 19 from both sides.
2t%5E2-3t-19+=+0 Solve this quadratic equation using the quadratic formula: t+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a and the a, b, and c, come from ax%5E2%2Bbx%2Bc+=+0
So here, a = 2, b = -3, and c = -19.
Make the substitutions:
t+=+%28-%28-3%29%2B-sqrt%28%28-3%29%5E2-4%282%29%28-19%29%29%29%2F2%282%29
t+=+%283%2B-sqrt%289-%28-152%29%29%29%2F4
t+=+%283%2B-sqrt%28161%29%29%2F4
t+=+%283%2F4%29%2B12.7%2F4 or t+=+%283%2F4%29-12.7%2F4
t+=+3.9 or t+=+-2.4
Only the positive answer is meaningful here, so...
It will take 3.9 seconds for the object to move 19 meters.