Find position of particle at certain time [solved]

[jwpaine]

A bee with a velocity vector r'(t) starts at (-1,5,-1) at t = 0 and flies around for 4 seconds. Where is the bee located at time 4 if

\(\displaystyle \int^4_0 r'(u)du = 0\)

I thought that using the FTC:

\(\displaystyle \int^4_0 r'(u)du = r(4) - r(0) = 0\)
\(\displaystyle r(0) = (-1, 5, -1)\)
\(\displaystyle r(4) - (-1, 5, -1) = 0\)
\(\displaystyle r(4) = (-1, 5, -1)\)

But of course this isn't correct.
Any help would be great.

EDIT: Ah, looks like that worked. I can't wait to get into more complicated things, but I also need to build up good foundations.

I keep all my posts for archiving purposes, never know when someone could learn form it

 

[Deleted member 4993]

A physics note to the problem:

r'(t) dt = ds that is incremental distance travelled.

If after 4 units of time - the total distance traveled is = 0 - then you must have come back to the initial position.

 

[fasteddie65]

A physics note to the problem:

r'(t) dt = ds that is incremental distance travelled.

If after 4 units of time - the total distance traveled is = 0 - then you must have come back to the initial position.

Just a slight correction: rather than the total distance, which can only be zero if the particle did not move, this is the position of the particle. Total distance would be found by integrating the absolute value of the velocity, just like total area would be found by integrating the absolute value of the function.

 

[Deleted member 4993]

A physics note to the problem:

r'(t) dt = ds that is incremental distance travelled.

If after 4 units of time - the total distance traveled is = 0 - then you must have come back to the initial position.

Just a slight correction: rather than the total distance, which can only be zero if the particle did not move, this is the position of the particle. Total distance would be found by integrating the absolute value of the velocity, just like total area would be found by integrating the absolute value of the function.

I stand corrected - wrong wording of explanation on my part. In this case ds is the magnitude of the displacement vector.