# Forces and vectors direction problem

In summary: I think the question is about displacement, not distance traveled. If the problem doesn't give the acceleration as a function of time, how can we solve for the distance traveled? :confused:In summary, the conversation discusses two forces acting on a particle at rest, and asks for the components of the particle's velocity, its direction, displacement, and coordinates at a specific time. The solution involves calculating the net force, using kinematic equations, and resolving the final velocity into x and y components. However, for part c, the displacement cannot be calculated without knowing the acceleration as a function of time.

## Homework Statement

Two forces, vector F 1 = (4i+ 6j) N and vector F 2 = (4i+ 8j) 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) In what direction is the particle moving at t = 10.3 s?

(c) What displacement does the particle undergo during the first 10.3 s?

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

## The Attempt at a Solution

For part a I tried dividing by the mass of the object to get Newtons to cancel to m/s^2
I also tried adding the two forces together, and adding -F2 to +F1 because in my textbook it says that once force is basically the opposite of the other
All of those were wrong
For part b, I took the arctan of 1.95 and -3.95 to get 63.7° but webassign said I was around 10% off on my answer
I haven't been able to do c or d yet
Any help or understanding as to what I did wrong would be greatly appreciated

...
For part a I tried dividing by the mass of the object to get Newtons to cancel to m/s^2
I also tried adding the two forces together, and adding -F2 to +F1 because in my textbook it says that once force is basically the opposite of the other
The net force is always the sum of all forces acting on a body, you don't have to worry about the directions vectors will take care of that themselves.
Calculate the net force and use that to get acceleration and then the rest is easy just resolve everything into x and y components and use the kinematic equations.

Enigman said:
The net force is always the sum of all forces acting on a body, you don't have to worry about the directions vectors will take care of that themselves.
Calculate the net force and use that to get acceleration and then the rest is easy just resolve everything into x and y components and use the kinematic equations.

So your saying I just need to add the two forces together to get the components of the particles velocity?
So Final F= (4i+6j)N + (4i+8j)N and that is what would be the answer for part a?
I did that though. That was my first attempt at an answer
And it came out wrong
Maybe I am not understanding calculating the net force?

So your saying I just need to add the two forces together to get the components of the particles velocity?
Noooo...
Components of force ≠ Components of velocity.
When you add the forces you get the net force which when you divide by mass you get the acceleration. Now you already know initial velocity is zero and you now have the acceleration too. So just use the kinematic equations.

Enigman said:
Noooo...
Components of force ≠ Components of velocity.
When you add the forces you get the net force which when you divide by mass you get the acceleration. Now you already know initial velocity is zero and you now have the acceleration too. So just use the kinematic equations.

Ohhhh got it
Duh haha
Lets see if I can get it

Enigman said:
Noooo...
Components of force ≠ Components of velocity.
When you add the forces you get the net force which when you divide by mass you get the acceleration. Now you already know initial velocity is zero and you now have the acceleration too. So just use the kinematic equations.

No :/
Ok so I found the Final F to be (8.00i+16.00j)N
Acceleration is [(8i+16j)N]/1.90kg
Or [(8i+16j)m/s^2]/1.9

Then I used the kinematic equation where Vf=Vi+at
Because the Vi is 0 and I know the acceleration and time
But its still wrong
?

No :/
Ok so I found the Final F to be (8.00i+16.00j)N
...
But its still wrong
?

1 person
No :/
Ok so I found the Final F to be (8.00i+16.00j)N
Acceleration is [(8i+16j)N]/1.90kg
Or [(8i+16j)m/s^2]/1.9

Then I used the kinematic equation where Vf=Vi+at
Because the Vi is 0 and I know the acceleration and time
But its still wrong
?
Please show us the details of your calculations to get the components of the velocity at 10.3 seconds. In your equation for the acceleration, why didn't you divide the 8 and the 16 by 1.9? Anyhow, the 16 should be a 14.

1 person
Enigman said:

Yeah I messed up with the addition, so its (8.00i+14.00j) right?

Chestermiller said:
Please show us the details of your calculations to get the components of the velocity at 10.3 seconds. In your equation for the acceleration, why didn't you divide the 8 and the 16 by 1.9? Anyhow, the 16 should be a 14.

In my calculations I did divide by 1.9
And yeah i fixed the 16 to a 14

Oh nevermind I got it
Thanks for helping guys :)

Actually quick question
For c and d

so c is asking for the displacement the particle undergoes during the first 10.3s?
Ive tried using the answer from part a for this part but every variation i use is wrong
The answer for a was (43.3i+75.9j) m/s
What am i doing wrong?

Actually quick question
For c and d

so c is asking for the displacement the particle undergoes during the first 10.3s?
Ive tried using the answer from part a for this part but every variation i use is wrong
The answer for a was (43.3i+75.9j) m/s
What am i doing wrong?

You can't use the velocity after 10.3 seconds to get the displacement after 10.3 seconds. That is because the velocity is changing during those 10.3 seconds. The velocity at time zero was zero. Show us the equations you are using to get the velocity and displacement. Show us your calculations in detail.

Chet

## 1. What is a force in physics?

A force is a push or pull on an object that can cause it to accelerate or change its motion. Forces are typically measured in Newtons (N) and have both magnitude and direction.

## 2. How do forces affect the motion of an object?

Forces can affect motion in three ways: they can make an object speed up, slow down, or change direction. This is known as Newton's First Law of Motion, which states that an object will remain at rest or in motion with a constant velocity unless acted upon by an external force.

## 3. What is a vector in physics?

A vector is a quantity that has both magnitude and direction. It is represented by an arrow, where the length of the arrow represents the magnitude and the direction of the arrow represents the direction of the vector. In the context of forces, vectors are used to represent the direction and magnitude of the force acting on an object.

## 4. How do you calculate the net force in a vector direction problem?

To calculate the net force in a vector direction problem, you must first determine the direction and magnitude of each individual force acting on the object. Then, you can use vector addition to find the resultant force, which is the net force acting on the object. The resultant force can be calculated using the Pythagorean theorem and trigonometric functions.

## 5. How do forces and vectors relate to Newton's Laws of Motion?

Forces and vectors play a crucial role in understanding and applying Newton's Laws of Motion. Newton's First Law states that an object in motion will remain in motion unless acted upon by an external force, and this external force can be represented as a vector. Newton's Second Law relates the net force acting on an object to its acceleration, and this can be calculated using vectors. Newton's Third Law states that for every action, there is an equal and opposite reaction, which can also be represented using vectors.