Question regarding position/displacement vectors

[PolyFX]

Homework Statement

The position of an object at three different times is given

At t= 4.9s
position= (4.0,3.1,0) m

At t= 5.4s
position = (1.3, 7.1, 0) m

At t= 5.9s
position = (-0.8,12.7,0) m

Using the best information available, what was the displacement of the bee during the time interval from 4.9 s to 4.93 s?

The earlier parts of this question asked for the average velocity of the object between 4.9s and 5.4 s (-5.4,8,0) m/s

And the average velocity between 4.9s and 5.9 s which is (-4.8, 9.6, 0) m/s.

Homework Equations

Displacement formula = r2 - r1 where r2 is the final position of the object and r1 is the initial position

and also,

r2 = r1 + (Average Velocity)(change in time)

The Attempt at a Solution

The way I attemped this solution is to use the average velocity between 4.9 s and 5.4 s (which was found earlier) and plug all the given values into the formula:

r2= r1 + (Average Velocity)(Change in time)

Which would be, (4.0,3.1,0) + ((-5.4,8,0)(0.93))
= (-1.022, 11.1, 0) = r2

I would then use this value for r2 into the formula for finding the displacement (r2 - r1)

(-1.022,11.1,0) - (4.0,3.1,0)

= (-5.022, 8, 0) m

So the final answer would be (-5.022, 8, 0) m

However, I'm still kind of sketchy on this solution and would just like some confirmation whether this is the right way of doing a question like this.

 

[mikelepore]

I get a different answer ..

Assuming the average velocity is the same for the interval 4.9 to 4.93 s
as it is for the interval 4.9 to 5.4 s ..

displacement for the interval 4.9 to 4.93 s =
(average velocity)(time interval) =
(-5.4,8,0) m/s multiplied by (4.93 s - 4.9 s)

 

[PolyFX]

I get a different answer ..

Assuming the average velocity is the same for the interval 4.9 to 4.93 s
as it is for the interval 4.9 to 5.4 s ..

displacement for the interval 4.9 to 4.93 s =
(average velocity)(time interval) =
(-5.4,8,0) m/s multiplied by (4.93 s - 4.9 s)

Wow mikelepore, I totally forgot about that equation for some reason. Thanks, the answer I got from your method is

(-0.162,0.24,0)

which makes much more sense. I just realized the magnitude for the displacement vector I had initially calculated was about 9.44 m which is almost double the magnitude of the displacement for the time interval between 4.9s and 5.4s, which doesn't seem to make sense for a question like this.

Thanks again.

 

[mikelepore]

Now I got the same answer as you.