# Pytels Dynamics 12.26: Block moves along the x-axis

• Alexanddros81
In summary, the problem involves a 0.1-kg block moving along the x-axis with a resultant force of -1.2tiN, where t is in seconds. When t=0, x=0 and v=54i m/s. The task is to determine the distance traveled by the block during the time interval t=0 to t=4s. The distance can be calculated by taking the integral of the speed with respect to time, which is the magnitude of the velocity. The velocity changes sign at t=3s, resulting in a total distance traveled of 128m.
Alexanddros81

## Homework Statement

A 0.1-kg block moves along the x-axis. The resultant of all forces acting on the block is F = -1.2tiN, where t
is in seconds. When t=0, x=0 and v=54i m/s.
Determine the distance traveled by the particle during the time interval t=0 to t=4s.

## The Attempt at a Solution

See the attached file.

Also, when do I use vector notation in the equations? Is it my choice whether to use it or not?
Next problem is with better pen.

#### Attachments

• Pytel_Dynamics025.jpg
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Alexanddros81 said:

## Homework Statement

A 0.1-kg block moves along the x-axis. The resultant of all forces acting on the block is F = -1.2tiN, where t
is in seconds. When t=0, x=0 and v=54i m/s.
Determine the distance traveled by the particle during the time interval t=0 to t=4s.

## The Attempt at a Solution

See the attached file.

Also, when do I use vector notation in the equations? Is it my choice whether to use it or not?
Next problem is with better pen.

The x(t) function is wrong.
The problem asks the distance traveled. It is not the same as the displacement, x(final)-x(initial).

The book gives a result of 128m.
Basicallly I am confused on how to calculate this. Do I calculate the position at every second (from 0 to 4 seconds) and then...?
Also x(t) should be ##x(t)=-2t^3+54t##
By looking the graph of the function when v=0 then t=3 and could be easily calculated.
At t=3s then x=108m. At t=4s then x=88m.
So the block had traveled from t=0s to t=3s to the right for 108m and then from t=3s to t=4s to the left for 20m. So distance travelled
from t=0s to t=4s is 128m.
How do I calculate this by using a formula?

Alexanddros81 said:
The book gives a result of 128m.
Basicallly I am confused on how to calculate this. Do I calculate the position at every second (from 0 to 4 seconds) and then...?
Also x(t) should be ##x(t)=-2t^3+54t##
By looking the graph of the function when v=0 then t=3 and could be easily calculated.
At t=3s then x=108m. At t=4s then x=88m.
So the block had traveled from t=0s to t=3s to the right for 108m and then from t=3s to t=4s to the left for 20m. So distance travelled
from t=0s to t=4s is 128m.
How do I calculate this by using a formula?
The distance traveled is the integral of the speed with respect to time. The speed is magnitude of the velocity ##v=|\vec v|##. The velocity changes sign at t = 3 s, so ##d=\int _0^3(-6t^2+54)dt+\int _3^4(6t^2-54)dt##

Alexanddros81
Yes. I've done the math and works fine. 108 from forst integral and 20 from second.

## 1. What is Pytels Dynamics 12.26?

Pytels Dynamics 12.26 is a mathematical model used to study the motion of objects along a specific axis, such as the x-axis. It takes into account various factors such as forces, mass, and acceleration to predict the movement of an object.

## 2. How does the block move along the x-axis?

The block's motion along the x-axis is determined by its initial position, velocity, and acceleration, as well as any external forces acting on it. The Pytels Dynamics 12.26 model can be used to calculate the position and velocity of the block at any given time.

## 3. What is the significance of the x-axis in this model?

The x-axis is used as a reference point to track the motion of the block. It allows us to study the motion of the block in one specific direction, without considering any motion in other directions. This simplifies the analysis and calculations involved in the model.

## 4. Can Pytels Dynamics 12.26 be applied to real-life situations?

Yes, Pytels Dynamics 12.26 can be applied to real-life situations where an object is moving along a specific axis, such as a car moving along a straight road or a ball rolling down a ramp. It provides a mathematical understanding of the motion and can be used to make predictions and solve problems.

## 5. What does the 12.26 in Pytels Dynamics 12.26 represent?

The 12.26 in Pytels Dynamics 12.26 represents the specific problem number in the textbook or course material where this model is introduced. It is often used to differentiate between different models and problems within the same subject.

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