# Solving Part c of Repulsive Force Homework Problem

• physics148
In summary, the conversation discusses the motion of a particle subjected to a repulsive force and asks for the general solution for the system, the values of constants for a specific initial position and velocity, and the initial velocity for a solution where the particle starts at a position and remains at rest. The solution involves finding an expression for the velocity as a function of time and taking the limit to find the initial velocity.
physics148

## Homework Statement

(2) Suppose a particle of mass m is subjected to a repulsive force F = +kx.
(a) What is the general solution for the motion of the system?
(b) If the particle begins with a position x(0) = x0 and with velocity v(0) = v0 at t = 0 what are the values of the constants appearing in the general solution?
(c) There is a solution where the particle starts at x0 and moves toward the origin only to remain
at rest there. What is the initial velocity v0?.

[/B]

## The Attempt at a Solution

So I solved part a) and b) and got (what I believe is the right answer) of
a) x(t)=C1e^(wt)+C2e^(-wt)
b)x(t)=(wx0+v0)e^(wt)/(2w)+(wx0-v0)e^(-wt)/(2w)

for part c, how would I go about solving it? I initiallly thought of equating velocity and position, since they are both equal when the particle is at rest, but I think I should instead somehow incorporate force, since the velocity will have to be negative to combat the positive repulsive force, but I'm uncertain on how to obtain v0.

Find an expression for the velocity as a function of time. Then you want to find at what v0 that expression goes to zero as time becomes very large.

Last edited:
awesome. figured it out by taking the limit. thanks!

## 1. What is the formula for calculating repulsive force?

The formula for calculating repulsive force is F = k(q1*q2)/r^2, where k is the Coulomb's constant, q1 and q2 are the magnitudes of the charges, and r is the distance between the two charges.

## 2. How do I determine the direction of the repulsive force?

The direction of the repulsive force is always away from the other charge. This means that if the charges are both positive or both negative, the repulsive force will be in the positive direction, and if the charges are opposite (one positive and one negative), the repulsive force will be in the negative direction.

## 3. How does distance affect the strength of the repulsive force?

The strength of the repulsive force is inversely proportional to the square of the distance between the two charges. This means that as the distance between the charges increases, the repulsive force decreases, and as the distance decreases, the repulsive force increases.

## 4. What is the unit of measurement for repulsive force?

The unit of measurement for repulsive force is Newtons (N). This is the same unit used to measure other types of forces, such as gravity and friction.

## 5. Can I use the same formula for calculating repulsive force in different situations?

Yes, the formula for calculating repulsive force is applicable in all situations where two charges are present. However, you may need to adjust the values of k, q1, and q2 depending on the specific scenario.

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