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A student has derived the following nondimensionally homogeneous equation: a=x/t2-vt+F/m where v is a velocity's magnitude , a is an acceleration's magnitude, t is a time, m is a mass, F is a force's magnitude , and x is a distance (or length). Which terms are dimensionally homogeneous? .
a) x/t
b) vt
c) a
d) F/m

Respuesta :

whitneytr12

Answer:

Letter C) and D) is the correct answer.

Explanation:

We know that the a is an acceleration's magnitude, so the units of a are m/s².

Now, let's analyze each terms. If we want that each term will be dimensionally homogeneous, all of them must have the same units of a.

[tex][\frac{x}{t}]=[\frac{m}{s}][/tex]

[tex][vt]=[m][/tex]

[tex][\frac{F}{m}]=[\frac{N}{kg}]=[kg\frac{m}{s^{2}kg}]=[\frac{m}{s^{2}}][/tex]

Therefore, the term F/m is the correct answer.

I hope it helps you!

pstnonsonjoku

We can see that  a and F/M are dimensionally homogeneous.

In solving dimensions, we try to express a quantity in terms of the fundamental quantities;

  • Mass
  • Length
  • Time

For the term a, its dimension is LT^-2

For the term F/m, its dimension is LT^-2

Hence, it follows that a and F/M are dimensionally homogeneous.

Learn more about dimensions: https://brainly.com/question/944206

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