Understanding Dimensional Analysis in Basic Linear Motion Formulas

In summary, As a new physics student, the speaker enjoys using formulas and has been experimenting with expressing them in terms of units instead of names. They have encountered difficulties when dealing with larger formulas and wonder if they are overthinking their approach. They also note that when only considering units, there may be a factor of 2 that is disregarded in the calculations.
  • #1
lozzajp
14
0
One thing I enjoy as a new physics student is using formulas. I have been playing with the fundamental formulas in terms of units rather than their names.

That is instead of a=v/t
m/s/s=(m/s)/s

or v=at
m/s=(m/s/s) x s
m/s=m/s

Simple maths yea, but when I am getting to the bigger formulas I am having trouble, perhaps they just don't work the way i am thinking but if someone could enlighten me that would be great..

S=(1/2)at^2
m=(1/2)x(m/s^2)x(s^2)
m=(1/2)x(m)

why do i get m = half m?

v^2 = 2as
m^2/s^2 = 2(m/s/s) x m
m^2/s^2 = 2 x m^2/s^2
m/s = 2 x m/s

again, there is a x2 factor there.

am i just thinking about this too much?
 
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  • #2
If you are only looking at the units you are throwing away any "dimensionless" constants in the formulas. From that point of view, there is not difference between "m" and "m/2"- both have dimensions of "meters" which is all you are looking at.
 

FAQ: Understanding Dimensional Analysis in Basic Linear Motion Formulas

What is lineal motion?

Lineal motion, also known as linear motion, is a type of motion where an object moves in a straight line with a constant velocity.

What are the basic lineal motion formulas?

The basic lineal motion formulas include distance (d) = velocity (v) x time (t), velocity (v) = displacement (d) / time (t), and acceleration (a) = change in velocity (Δv) / time (t).

How do these formulas relate to each other?

The first formula (distance = velocity x time) is used to calculate the distance an object travels when its velocity and time are known. The second formula (velocity = displacement / time) is used to calculate the velocity of an object when its displacement and time are known. The third formula (acceleration = change in velocity / time) is used to calculate the acceleration of an object when its change in velocity and time are known.

What are the units for the variables in these formulas?

The units for distance (d) is typically meters (m), velocity (v) is typically meters per second (m/s), time (t) is typically seconds (s), displacement (d) is typically meters (m), change in velocity (Δv) is typically meters per second (m/s), and acceleration (a) is typically meters per second squared (m/s^2).

How are these formulas applied in real-world situations?

The basic lineal motion formulas are often used in physics and engineering to analyze and predict the motion of objects in real-world situations. This can include calculating the distance and velocity of a moving car, or the acceleration of a falling object due to gravity. They are also used in designing and optimizing machinery and vehicles that require precise motion control.

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