Find the powers p and q that make this equation dimensionally consistent

  • Thread starter swatmedic05
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In summary, the equation for acceleration (A) is related to velocity (V) and time (t) by the expression A=V^p t^q. To make this equation dimensionally consistent, we need to find the powers p and q. By equating the exponents on both sides, we can determine that p=1 and q=2. This means that the units for acceleration are [length]/[time]^2, the units for velocity are [length]/[time], and the units for time are [time]. By understanding the units and their exponents in the equation, we can make sure that it is dimensionally consistent.
  • #1
swatmedic05
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Acceleration is related to velocity and time by the following expression: A=V^p t^q

Find the powers p and q that make this equation dimensionally consistent.
 
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  • #2
So what dimensions are A, V and t ?

When you get that, then equate exponents.
 
  • #3
I new to physics I still don't get what I have to do
 
  • #4
swatmedic05 said:
I new to physics I still don't get what I have to do

Alright then. Let's start simple.

What are the units for acceleration (A)?

What are the units for velocity (V)?

What are the units for time (t) ?
 
  • #5
A= [l]/[t]^2
v= [l]/[t]
t=[t]
 
  • #6
swatmedic05 said:
A= [l]/[t]^2
v= [l]/[t]
t=[t]

Good. So in A=Vptq, on the left side we have

LT-2

and on the right we have

(LT-1)p(T)q

What does the right side give?
 
  • #7
I just got it now... Thank you for explaining it better to me. I appreciate all your help
 

1. What is dimensional consistency?

Dimensional consistency is the concept that all terms in an equation must have the same units in order for the equation to be mathematically and physically valid. In other words, the dimensions (such as length, time, mass, etc.) on both sides of the equation must match.

2. Why is dimensional consistency important?

Dimensional consistency is important because it ensures the accuracy and validity of equations in science and engineering. If an equation is not dimensionally consistent, it means that there is an error in the units or dimensions used, which can lead to incorrect results and conclusions.

3. How do you determine if an equation is dimensionally consistent?

To determine if an equation is dimensionally consistent, you must check the units and dimensions of each term on both sides of the equation. If they are the same, then the equation is dimensionally consistent. If they are not the same, then the equation is not dimensionally consistent and you must adjust the units or dimensions of one or more terms to make them match.

4. What are the powers p and q in this equation?

The powers p and q in an equation represent the dimensions of the terms in the equation. For example, in the equation F = ma (force = mass x acceleration), the powers of m and a are both 1, indicating that they have the dimensions of mass and acceleration, respectively. These powers must be adjusted to make the equation dimensionally consistent.

5. How do you find the powers p and q that make an equation dimensionally consistent?

To find the powers p and q, you must analyze the dimensions of each term in the equation and determine what powers are needed to make them match. This can involve using conversion factors or rearranging the equation to make the dimensions match. Once the dimensions are consistent, the equation is considered dimensionally consistent and the values of p and q can be determined.

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