# Forces, displacement, and coordinates of a particle

In summary: The magnitude of the vector is the length of the vector from the origin to the point(s) in question.In this case, the magnitude is the length of the vector from the origin to the point (60.29°, -3.95 m).

## 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 can't remember, but nothing has come out right.

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

voko said:
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?

voko said:
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 I am 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.

voko said:
Then it is probably the magnitude.

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

Right.

1 person
Ok sorry for all the questions but i just want to make sure I am going to do this right

So I solve for Δr and put those under the radical sign?
But since those are vector components I can't 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?

## 1. What is a force?

A force is a push or pull that can cause an object to accelerate or change its motion. It is measured in units of Newtons (N).

## 2. How is displacement different from distance?

Displacement refers to the change in position of an object from its original starting point to its ending point. Distance, on the other hand, refers to the total length of the path that the object has traveled. Displacement is a vector quantity, meaning it has both magnitude and direction, while distance is a scalar quantity, only having magnitude.

## 3. What are coordinates of a particle?

The coordinates of a particle refer to the specific location of the particle in a given coordinate system. This can be represented by a set of numerical values, such as (x, y) or (x, y, z), where each coordinate corresponds to a different dimension.

## 4. How do forces affect the motion of a particle?

Forces can cause a particle to accelerate, decelerate, or change direction. The specific effect depends on the magnitude and direction of the force, as well as the mass and initial velocity of the particle. Newton's Second Law states that the acceleration of a particle is directly proportional to the net force acting on it and inversely proportional to its mass.

## 5. How is displacement related to velocity?

Displacement and velocity are closely related as velocity is the rate of change of displacement over time. In other words, velocity is the displacement of an object divided by the time it took to travel that distance. This relationship is expressed by the equation v = Δx/Δt, where v represents velocity, Δx represents displacement, and Δt represents time.