# Motion of a particle and zero velocity

• Alexanddros81
In summary, the motion of a particle is defined by the relation ##x = 2t^3 - 15t^2 + 24t + 4## where x is expressed in meters and t in seconds. We can determine that the velocity is zero when t=3, and the position and total distance traveled when the acceleration is zero by solving for x and taking the difference between x at t=2.5 and t=1. The total distance traveled is 24.5 meters.
Alexanddros81

## Homework Statement

11.7 The motion of a particle is defined by the relation ##x = 2t^3 - 15t^2 + 24t + 4
where x is expressedin meters and t in seconds. Determine (a) when the velocity zero ,
(b) the position and the total distance traveled when the acceleration is zero

## The Attempt at a Solution

[/B]
Can you check if my solution is correct?

#### Attachments

• Vector Mechanics Dynamics Beer P11_7 s.jpg
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Alexanddros81 said:

## Homework Statement

11.7 The motion of a particle is defined by the relation ##x = 2t^3 - 15t^2 + 24t + 4
where x is expressedin meters and t in seconds. Determine (a) when the velocity zero ,
(b) the position and the total distance traveled when the acceleration is zero

## The Attempt at a Solution

View attachment 222710
[/B]
Can you check if my solution is correct?
First, let me comment that your printing is neat and readable in the image. However, you are much more likely to get responses to your questions if you type in your solution. Many helpers will not respond otherwise.

That said, yes, your solution looks correct.

Looks good to me.

Is my last sentence correct?

I think it should be ##x(2.5) - x(1) = 1.5 - 15 = -13.5## (moving in opposite direction).
Overall though the particle travels a total distance of 11+13.5 = 24.5

## What is motion?

Motion is the change in position of an object over time. It can be described using variables such as displacement, velocity, and acceleration.

## What is a particle?

A particle is a small, localized object that can be treated as a single point in space. It has mass and can undergo motion.

## What does zero velocity mean?

Zero velocity, also known as rest or stationary, means that the particle is not moving. Its displacement remains constant over time.

## Can a particle have zero velocity and still be in motion?

Yes, a particle can have zero velocity and still be in motion. This is known as uniform motion or constant velocity. In this case, the particle is moving at a constant speed in a straight line.

## How is zero velocity different from zero acceleration?

Zero velocity means that the particle is not moving, whereas zero acceleration means that the particle's velocity is not changing. This means that the particle may be moving at a constant speed, but its direction may be changing.

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