# A particle traveling question

• singedang2
In summary, the conversation discusses how to show that, during a trip where a particle travels a unit distance in a unit amount of time and starts and ends at rest, the magnitude of the particle's acceleration was at least 4 at some point. The solution involves using the concept of kinematics and the mean value theorem to show that the acceleration must reach at least 4 at some point during the trip.
singedang2

## Homework Statement

A particle travels a unit distance in a unit amount of time. It starts at rest and ends at rest.

I need to show that, at some time during the trip, the magnitude of the particle’s
acceleration was at least 4.

## The Attempt at a Solution

i really don't know how to do this problem. any hints?

help pls. thanks!

Hint: Imagine the particle accelerating uniformly for the first half of the distance, then decelerating uniformly during the second half.

so how am i supposed to show that? a/2 + (-a/2) = ??/

Given my hint, what acceleration does it imply? Use your knowledge of kinematics to relate distance, time, and acceleration.

so you're saying i need to show that while it was accelerating for the first half, the magnitude was 4?
and i don't clearly get what it means to travel unit distance in a unit amount of time. isn't unit normally mean 1?

singedang2 said:
so you're saying i need to show that while it was accelerating for the first half, the magnitude was 4?
Right. That's the gentlest way to accelerate and will give you the minimum acceleration.
and i don't clearly get what it means to travel unit distance in a unit amount of time. isn't unit normally mean 1?
Sure, what's the problem? Distance = 1 unit. (That unit distance could a meter, a foot, 25.3 miles, whatever... doesn't matter! Call it 1 distance unit.)

Same for time.

Whatever the unit is, speed is measured in Distance Units/Time units; acceleration will be in Distance units/Time units squared.

Cut the distance interval in half. show that at least one of the interval takes less than 1/2 a minute to travel through. Then show that in that interval, the average velocity must be at least some value. Then, using the mean value theorem, at some point in the interval, the speed must be that value. use similar arguments to show that the acceleration must be at least some value (namely 4) in some interval.

## 1. What is a particle traveling question?

A particle traveling question refers to a question that involves the motion and/or behavior of a particle in a given scenario or system. It may involve concepts such as velocity, acceleration, forces, and interactions between particles.

## 2. How do I solve a particle traveling question?

To solve a particle traveling question, you will need to use equations and principles from physics, such as Newton's laws of motion and the kinematic equations. You will also need to identify the given parameters, such as initial and final velocities, and use them to solve for the unknown variables.

## 3. What is the difference between a particle traveling question and a particle at rest question?

A particle traveling question involves a particle that is in motion, while a particle at rest question involves a particle that is not moving. In a traveling question, you will need to consider the particle's velocity and acceleration, while in a particle at rest question, you will only need to consider the forces acting on the particle.

## 4. Can I use calculus to solve particle traveling questions?

Yes, calculus can be used to solve particle traveling questions, particularly when the particle's motion is not constant. In these cases, you can use calculus concepts such as derivatives and integrals to determine the particle's velocity and position at a given time.

## 5. How do I interpret the results of a particle traveling question?

The results of a particle traveling question will typically include values for the particle's displacement, velocity, and acceleration. These values can be used to determine the direction and magnitude of the particle's motion, as well as any changes in its motion over time.

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