# Forces and vectors direction problem

## 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 havent been able to do c or d yet
Any help or understanding as to what I did wrong would be greatly appreciated

Enigman
.....
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. 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 Im not understanding calculating the net force?

Enigman
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.

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

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
????

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

• 1 person
Mentor
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

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

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?

Mentor
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