anonymous
  • anonymous
position for an object given s(t)=2t^2-6t-4, what is the total distance travelled on [1,4]
Precalculus
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
The object's position at t = 1 is: \[2(1)^2 - 6(1) -4 =-8\] The object's position at t = 4 is \[2(4)^2 - 6(4) - 4 = 4\]
anonymous
  • anonymous
The difference between the initial and final positions is: \[x_f - x_i = 4 - (-8) = 12\]
anonymous
  • anonymous
Interestingly, though, if you put a pedometer on the object, that would not be what it measures.

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anonymous
  • anonymous
The object's motion is given by: \[s = 2t^2 - 6t - 4\] This is a parabola, which has a vertex at \[t =3/2\] which means that the object actually turns around at t = 3/2
anonymous
  • anonymous
A pedometer on the object would measure the sum of the distance traveled between the intervals [1,3/2] and [3/2, 4].
anonymous
  • anonymous
The object's position at t = 3/2 is: \[ 2(1.5)^2 - 6(1.5) - 4 = -8.5\]
anonymous
  • anonymous
So, between 1 and 3/2, the object travels .5, and between 3/2 and 4 it travels 12.5
anonymous
  • anonymous
A pedometer placed on this object would measure that the object traveled 13 units
anonymous
  • anonymous
I don't know which answer the question wants, 12 or 13. It is probably 12, but I am not sure.
anonymous
  • anonymous
Rhanks so much!
anonymous
  • anonymous
You are welcome

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