Question

Assume v(t) = 6t - 18 on the interval [0, 6]. Find the total distance that the object traveled on [0, 6].

Answer 1

we just did one of these

x(t) = 3t^2 - 18t + c

Now just figure x(6)-x(0)

Answer 2

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

Answer 3

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

Answer 4

See Baggins, Bilbo, "There and Back Again".

Answer 5

So is the total distance 54?

Answer 6

yes