# Forces, displacement, and coordinates of a particle

## Homework Statement

Two forces, vector F 1 = (4 i hat bold + 6 j hat bold) N and vector F 2 = (4 i hat bold + 8 j hat bold) N, act on a particle of mass 1.90 kg that is initially at rest at coordinates (+1.95 m, -3.95 m).

A) What are the components of the particle's velocity at t = 10.3 s?
B) What are the components of the particle's velocity at t = 10.3 s?
C) What displacement does the particle undergo during the first 10.3 s?(Δr)

D) What are the coordinates of the particle at t = 10.3 s?

## The Attempt at a Solution

For C) I have tried every method I could think of to solve for Δr from multiplying the components of the particles velocity (A) by the time, to squaring each part and placing them under a √
D) I tried a lot for D too. I tried multiplying the coordinates given in the problem above by time, multiplying by the velocity components, and some other methods I cant remember, but nothing has come out right.

The section titled "relevant equations" is there for a reason. What equations are relevant in this case?

The section titled "relevant equations" is there for a reason. What equations are relevant in this case?

If i knew I would use them

For A) I used F=ma
Vf=Vi+at
For B) I used arctan (Vxf/Vyf)

For C) the equation I thought might be right was rf=ri + Vit + 1/2at^2, but that was wrong

And for D) I tried to multiply the time by the velocity components because the seconds would cancel out and I'd be left with meters

The equation you mentioned for C) is indeed the equation you should have used. What was the problem with it?

The equation you mentioned for C) is indeed the equation you should have used. What was the problem with it?

Im not sure, I can try it again
I think I may have been confused on what numbers get plugged in where

So t=10.3s
a=4.21i+7.36j m/s^2
Vi=0?
And then im solving for rf-ri

Is that all correct?

You will obtain the displacement vector. It is not entirely clear to me whether C) wants that, or its magnitude, though.

Its asking for Δr in meters

Then it is probably the magnitude.

Then it is probably the magnitude.

Thats where you square the values and put them under the radical sign right?

Right.

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Ok sorry for all the questions but i just wanna make sure im gonna do this right

So I solve for Δr and put those under the radical sign?
But since those are vector components I cant add them together
Am i putting the wrong values under the rad sign?

If you are given a vector ## a \vec \imath + b \vec \jmath##, what is its magnitude?