# Particle Motion Analysis: Solving for Position and Velocity

• XPX1
In summary, a particle passes through the origin with an initial speed of 5.6 m/s in the positive y direction. The particle accelerates in the negative x direction at 5.2 m/s2. The particle's x and y positions after 4.0 seconds are 238.72 meters.
XPX1
A particle passes through the origin with an initial speed of 5.6 m/s in the positive y direction. The particle accelerates in the negative x direction at 5.2 m/s2.
(a) What are its x and y positions after 4.0 s?
m (x position)
m (y position)
(b) What are vx and vy at this time?
m/s (vx)
m/s (vy)

This question seems pretty hard to me, I have tried about 4 times to get the answer to no avail, here's what I have done.

To try and find out where its x and y positions were after 4.0 seconds, I plugged it into the Position Versus Time Equation, xf=xi+vixt+.5axt^2

Since I have the givens

time = 4.0
Vi=5.6
a=-5.2^2

I plug it into the equation.

xf=xi+vixt+.5axt^2

xf=0+5.6(4)+.5(-5.2)^2(4.0)^2

xf=238.72

however, this answer for part A. was not correct.

Can anyone tell me what I am doing wrong here?

You have to treat each direction separately.
you will have two equations
eq 1: xf=xi+vixt+.5axt^2
eq 2: yf=yi+viyt+.5ayt^2
think about what the question says and in which direction each velocity and acceleration is in.

Aaahh.. I see, so if it is going in the x direction at -5.2m/s^2 then after 4 seconds, it would be xf=0+0+.5(-5.2)^2(4)^2?

and if it is going in the y direction

yf=0+5.6(4)+.5(?)(4)^2

So, how do I figure out the y if I am not given the acceleration?

If you're not given an acceleration, I think you can assume that there is none and the particle is moving at a constant velocity in the y direction.

I got the final position of the y correct, but for x I am still lost.

if X is accelerating at -5.2m/s^2, where will it be in 4 seconds?

I plugged it into the position versus time equation

xf=0+0+.5(-5.2)^2(4)^2
xf=216.32

The above answer was false, I am completely lost on this, thanks for your help on solving the y position though conquer!

xf=xi +vixt +.5a(t^2)
compare that to your equation
"xf=0+0+.5(-5.2)^2(4)^2"
you have something I don't...

what am I missing? I still don't see what I have that you dont

heh, take a look at the acceleration...after everythign cancels, you have
xf=.5(a^2)(t^2)
I have
xf=.5(a)(t^2)

But.. its 5.2 meters a second squared, so doesn't that make it 5.2^2? or do I take the square root of 5.2 and put it into a?

xf=.5(-5.2^2)(4^2)

or...

xf=.5(2.28)(4^2)?

okay, here's the units:
acceleration = m/s^2
t^2 = s^2
so
a x t^2 = m/s^2 x s^2 = m

so it's just xf = .5(-5.2)(4^2), this will give you your answer in meters.

a is already in m/s^2, if you square it again, your units would be m^2/s^4

Ah thanks, that was correct! I still don't quite understand why you don't leave it m/s^2 though

XPX1 said:
I still don't quite understand why you don't leave it m/s^2 though
hmm... I'm not sure what you mean by this.
You ARE leaving the acceleration in m/s^2 because by definition, acceleration is in m/s^2. Doing anything to that acceleration would change the formula.
You don't want the final answer in m/s^2 because you have a distance, x, which should be in meters, on the other side of the equation.

maybe there's someone else in the forums who can explain this more clearly... anybody care to give it a try?

I think I understand it now, thanks for all your help!

## What is homework?

Homework is a set of academic tasks given to students by their teachers to complete outside of class time. It is designed to reinforce and extend the concepts learned in the classroom.

## What is a particle question?

A particle question is a type of question that asks about a specific detail or component of a larger concept or problem. It is often used in scientific research to narrow down and focus on a specific aspect of a topic.

## Why is homework important?

Homework is important because it helps students practice and apply the concepts they have learned in class. It also helps students develop important skills such as time management, critical thinking, and problem-solving.

## How do particle questions help in scientific research?

Particle questions help in scientific research by breaking down larger concepts into smaller, more manageable components. This allows researchers to focus on specific aspects of a topic and gather more precise and detailed information.

## Is there a recommended method for completing homework and particle questions?

There is no one recommended method for completing homework and particle questions. It is important to find a study method that works best for each individual, whether it be working in a group, using flashcards, or creating outlines. The key is to find a method that helps you understand and retain the information effectively.

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