How to find the dimensions of a particle moving in one dimension?

In summary, the dimensions of the constants alpha, beta, and gamma in the equation x(t) = (alpha)t^2 + (beta)t + (gamma) are determined by the units of x(t). For example, the units of beta·t must agree with the units of x(t).
  • #1
kratos
5
0
So a particle of mass M is moving in one dimension given by:
x(t) = (alpha)t^2 + (beta)t + (gamma)

where alpha, beta, gamma are non zero constants.

What are the dimensions of the alpha, beta, gamma?

Either the answer is staring right at my face or my physics is rusty :/
 
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  • #2
This looks like one of the equations of motion for a particle moving in the x direction.

[itex]x(t) = ut + \frac{at^2}{2}[/itex]
 
  • #3
kratos said:
So a particle of mass M is moving in one dimension given by:
x(t) = (alpha)t^2 + (beta)t + (gamma)

where alpha, beta, gamma are non zero constants.

What are the dimensions of the alpha, beta, gamma?

Either the answer is staring right at my face or my physics is rusty :/
Welcome to Physics Forums.

Okay, let's look at the beta term as an example:

The units of beta·t must agree with the units of x. So we can write
beta·t ~ x​
Where "~" means they have the same units, not that they are equal. But, we can solve this as if it were an equation. So, solving for beta, what do you get?
 

Related to How to find the dimensions of a particle moving in one dimension?

1. How do you measure the dimensions of a particle moving in one dimension?

The dimensions of a particle moving in one dimension can be measured using a ruler or a measuring tape. The position of the particle can be marked at different points in time, and the distance between these points can be measured to determine its dimensions.

2. What units are used to measure the dimensions of a particle?

The dimensions of a particle moving in one dimension are typically measured in meters (m) or centimeters (cm). These units represent the distance traveled by the particle along the one-dimensional axis.

3. Can the dimensions of a particle change as it moves in one dimension?

No, the dimensions of a particle remain constant as it moves in one dimension. This is because the particle is only moving along a single axis and does not change in size or shape.

4. How can the dimensions of a particle be represented graphically?

The dimensions of a particle moving in one dimension can be represented on a graph by plotting the position of the particle on the vertical axis and time on the horizontal axis. The slope of the line connecting these points represents the velocity of the particle.

5. Are there any mathematical equations to calculate the dimensions of a particle moving in one dimension?

Yes, the dimensions of a particle moving in one dimension can be calculated using the equation d = v * t, where d is the distance traveled, v is the velocity, and t is the time. This equation can be used to determine the dimensions of a particle at any given time.

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