Question
Assume v(t) = 6t - 18 on the interval [0, 6]. Find the total distance that the object traveled on [0, 6].
Answers
Steve
we just did one of these
x(t) = 3t^2 - 18t + c
Now just figure x(6)-x(0)
x(t) = 3t^2 - 18t + c
Now just figure x(6)-x(0)
Jamie
I got 0. That doesn't make sense to me...
x(0) = 3(0)^2 - 18(0) + C = 0+C
x(6) = 3(6)^2 - 18(6) + C = 108-108+C = 0+C
x(6)-x(0)=0
x(0) = 3(0)^2 - 18(0) + C = 0+C
x(6) = 3(6)^2 - 18(6) + C = 108-108+C = 0+C
x(6)-x(0)=0
Damon
Your velocity is zero at t = 3 !!!!!
right in the middle of your range.
It reversed direction midstream
You calulated displacement (where it moved to which was nowhere)
instead of how far it went (distance moved)
do t = 0 to t = 3
then t = 3 to t = 6
add the ABSOLUTE VALUES
right in the middle of your range.
It reversed direction midstream
You calulated displacement (where it moved to which was nowhere)
instead of how far it went (distance moved)
do t = 0 to t = 3
then t = 3 to t = 6
add the ABSOLUTE VALUES
Damon
See Baggins, Bilbo, "There and Back Again".
Jamie
So is the total distance 54?
Damon
yes