Distance between 2 particles

• mrkb80
In summary, the rate of change of the distance between the two particles at time t = pi can be found by first calculating the distance between them using the pythagorean theorem. Then, taking the directional derivative will give the rate of change. If the rate of change is positive, the particles are getting farther apart, and if it is negative, they are getting closer together.

Homework Statement

The position of a particle at time t is given by r(t) = 3(t2 - sin t)i +
tj - (cos t)k , and the position of another particle is R(t) = t2i + (t3 +
t)j+(sin t)k . At time t = pi, what is the rate of change of the distance
between the two particles? Are they getting closer to one another, or
are they getting farther apart?

The Attempt at a Solution

I'm actually not sure how to attempt this problem. I think that if the rate of change is postive they are getting farther apart and if it is negative they are getting closer, but I'm not sure.

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The first thing you need to do is write an expression for the distance between the two particles. Think pythagorean theorem.

I'm not sure I understand. Do I subtract the square of the i,j,k components from each other to get d^2 and then take the directional derivative?

1. What is the distance between two particles?

The distance between two particles is the length of the straight line connecting the centers of the two particles. It is typically measured in meters (m) or nanometers (nm) for microscopic particles.

2. How is the distance between two particles calculated?

The distance between two particles can be calculated using the distance formula, which is the square root of the sum of the squares of the differences in the x, y, and z coordinates of the two particles. This formula is derived from the Pythagorean theorem.

3. Can the distance between two particles change?

Yes, the distance between two particles can change if the particles are in motion or if there are external forces acting on them. For example, the distance between two electrons in an atom can change when the atom is excited.

4. How does the distance between two particles affect their interactions?

The distance between two particles can affect the strength of their interactions. As the distance between two particles decreases, the force of attraction or repulsion between them increases. This is because the particles are closer together and their electric charges or masses have a greater influence on each other.

5. Is there a minimum distance between two particles?

In classical physics, there is no minimum distance between two particles. However, in quantum mechanics, there is a concept known as the "zero-point energy" which implies that particles cannot be at a distance of exactly zero. There will always be a small but non-zero distance between them.