# A particle of mass m kg is acted on by two forces F1 and F2 with magnitudes 3root5 newtons and root5 newtons ad drections parallel to the vectors i+2j and i-2j respectively

The particle is initially at a position given by vector 2i+j

iv calculated the cartesian components of F1 and F2
F1 = 3i+6j
F2 = i 2j

iv also calculated the cartesian component of the total force F1+F2 = (3i+6j)+(i-2j) = 4i +4j

however the part im struggling on is that now the particle is of mass 1kg and is initially at rest, i have to use newtons 2nd law to write down an equation of motion and find the position of the particle after 1second.

so far iv tried:
F=ma
F1+F2= 1a
therefore a = 4i+4j but then i don't know how to find the new posistion ...can anyonehelp thankz

New postion= oldposition +intialvelocity*time + 1/2 acceleration*time^2. Technically, you should integrate to get this equation, but because acceleration is constant, the integration leads to the preceeding.

where acceleration= force/mass, and you have force and mass.

all the above of course is a vector equation, not messy at all. You can work the i,j components as separate equations, as the system is orthogonal. If needed, I can critique your work.

thankz iv worked it out

Assuming you have calculated the "a" vector correctly, just multiply it by t^2 to get the vector position change at time t. You do not have to add a term for (initial velocty vector) times t,, because the mass was initially at rest.

Add the position change vector to the initial position coordinates to get the new location.

I forgot about the factor (1/2) when calculating the position change due to acceleration. Bob Pursley's answer, posted just before mine, is correct

I have no clue.

9 months ago

## No worries, I can explain it to you step by step.

First, you correctly calculated the cartesian components of the total force, which is F = 4i + 4j.

To find the acceleration, you can use Newton's second law, F = ma, where F is the total force and m is the mass of the particle. In this case, the mass is 1 kg.

So, you have F = ma, and you already have F = 4i + 4j. Now, divide both sides of the equation by the mass, m = 1:

4i + 4j = a(1)

This gives you the acceleration vector a = 4i + 4j.

To find the position of the particle after 1 second, you can use the equation of motion:

New position = old position + initial velocity * time + (1/2) * acceleration * (time^2)

Since the particle is initially at rest, the initial velocity is 0, so that term becomes 0.

So the equation becomes:

New position = old position + (1/2) * acceleration * (time^2)

Plugging in the values, old position = 2i + j, acceleration = 4i + 4j, and time = 1, you can calculate the new position:

New position = (2i + j) + (1/2)(4i + 4j)(1^2)

Simplifying the calculation:

New position = 2i + j + 2i + 2j

New position = 4i + 3j

Therefore, the new position of the particle after 1 second is given by the vector 4i + 3j.

I hope that clarifies it for you! Let me know if you have any further questions.