Calculating Velocity from Vector Addition of Ion Positions

[Gold3nlily]

Homework Statement

An ion's position vector is initially r> = (5.0m)i - (6.0m)j = (2.0m)k and 10 s later it is r> = (-2.0m)i +(8.0m)j - (2.0m)k. In unit-vector notation, what is its during the 10 s?

The answer is supposed to be r> = (-0.7m/s)i + (1.4m/s)j - (0.4m/s)k (from back of my book) but I keep getting r> = (0.3m/s)i + (0.2m/s)j

Homework Equations

Vave> = r> (total) / T (total)

The Attempt at a Solution

r> = (5.0m)i - (6.0m)j = (2.0m)k
r> = (-2.0m)i +(8.0m)j - (2.0m)k.
+ -----------------------------
r> (total) = (3.0m)i + (2.0m)j

Vave> = r> (total) / T (total)
Vave> = (3.0m)i + (2.0m)j / 10sec
r> = (0.3m/s)i + (0.2m/s)j

I know my error doesn't have to do with the units, becasue I still end up with m/s in my answer. So where then did I go wrong?

 

[PhanthomJay]

The displacement is the final position minus the initial position. You semed to have just added up the position vectors.

 

[Gold3nlily]

The displacement is the final position minus the initial position. You seemed to have just added up the position vectors.

Ah! That makes sense.

But I'm confused- my book says r>(total) = r1> + r>2 ...+ r_n>

What makes this problem different than say this problem I will post at the bottom. In this other problem it was necessary to add the vectors instead of subtract. Is that becasue the problem you helped me with works with "position" vector and the problem at the bottom of the page works with some other type of vectors?

other problem:
"A train at a constant 60.0 km/h moves east for 40.0 min, then in a direction 50.0° east of due north for 20.0 min, and then west for 50.0 min. What are the (a) magnitude and (b) angle of its average velocity during this trip?"

Btw- I subtracted the vector and got the correct answer. Thank you.

 

[PhanthomJay]

Yes, the position vector specifies a point in reference to a coordinate system with its origin at (0,0,0), as in the first problem. The second problem uses displacement vectors.

Suppose you had a particle with an initial position vector of 2i + 2j, and a final position vector of 2i + 3j. Its displacement is obtained by subtracting the initial position vector from the final position vector, such that its displacement is just j (or 1 unit [N]). But if a a particle was displaced 2i +2j units and then 2i + 3j units, its displacement would be 4i + 5j. A quick sketch helps.

 

[Gold3nlily]

Thank you very much. I get it now.