# Distance of particle travels from origin, and maximum speed, picture included

• gap0063
In summary: The potential energy at x=0 is 0, as it is the starting point where the potential energy is defined to be 0. In summary, a 3.2 kg particle is moving under the influence of a force described by the potential energy function U = α|x|, with a = 5.48 J/m. The total energy of the particle is 18 J and it also has kinetic energy. To find the distance traveled before reversing direction, we can use the equation K_initial + U_initial = K_final + U_final. At x=0, the potential energy is 0, so the initial potential energy is also 0. This means that the initial kinetic energy is equal to the total energy,
gap0063

## Homework Statement

A 3.2 kg particle moves along the direction
under the influence of a force described by the
potential energy function U = a k~xk, where
a = 5.48 J/m and x is the position of the
particle in meters measured from the origin
as in Figure.
The total energy of the particle is 18 J.
[PLAIN]http://img828.imageshack.us/img828/2877/problem9.jpg
(a) Determine the magnitude of the distance
that the particle travels from the origin before
reversing direction.
(b)Find the maximum speed of the particle.

## Homework Equations

Not sure
the only equation I know with distance is $$\Delta$$Emech=-fkd

## The Attempt at a Solution

So I know the total energy is 18 J
but there is no u
and there is no velocity...maybe i can turn acceleration into velocity?

Last edited by a moderator:
The force is conservative as there is potential energy. In case of conservative forces, the total mechanical energy is conserved. You know the potential energy, U=α|x|. What other energy does the particle have?

ehild

ehild said:
The force is conservative as there is potential energy. In case of conservative forces, the total mechanical energy is conserved. You know the potential energy, U=α|x|. What other energy does the particle have?

ehild

it also has kinetic energy?

so Ki+Ui=Kf+Uf?

Yes!

ehild

ehild said:
Yes!

ehild

I'm still confused... what part is Uf and what part is Ui

and I don't know how to calculate kinetic energy without velocity

What is the PE at x=0?

ehild

## 1. What is the distance traveled by a particle from its origin?

The distance traveled by a particle from its origin is determined by its displacement, which is the shortest distance between the starting point (origin) and the ending point (final position).

## 2. How is the distance of a particle's travel calculated?

The distance of a particle's travel can be calculated by finding the magnitude of its displacement vector, which involves calculating the differences between the final and initial coordinates of the particle.

## 3. What is the maximum speed of a particle?

The maximum speed of a particle is the highest velocity it reaches during its travel. It is determined by the rate of change of its position over time.

## 4. How is maximum speed related to distance traveled?

The maximum speed of a particle is directly related to the distance it travels. The longer the distance, the higher the maximum speed, and vice versa.

## 5. How can the distance and maximum speed of a particle be represented visually?

The distance and maximum speed of a particle can be represented on a graph, with distance on the x-axis and maximum speed on the y-axis. The distance traveled can be shown as a line or curve, while the maximum speed can be represented as a point or line on the graph.

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