Question

A student has derived the following nondimensionally homogeneous equation:a=xt2−vt+Fmwhere 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?

Answer 1

These are the terms that are dimensionally homogenous:

x/t^2

F/m

a

Step-by-step explanation:

Before making any comparisons, first reduce each term to its base SI units. Given that acceleration is a change in length per square of unit time, what are the units of acceleration?

Ans: (m/s^2)

If the magnitude of the force F is in N and the mass m is in kg, what are the units of the term F/m?

Ans: (m/s^2)

If the distance x is in m and the time t is in s, what are the units of the term x/t^2?

Ans: (m/s^2)

If the velocity's magnitude v is in m/s and the time t is in s, what are the units of the term vt?

Ans: (m)

Therefore, x/t^2, F/m, and a are the correct answers.

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Answer 2

None of the terms are dimensionally homogeneous

Step-by-step explanation:

`a=xt^(2)-vt+Fm`

dimensions from each term:

`a:(L)/(T^(2))`

`xt^(2):L*T^(2)`

`vt:(L)/(T)*T=L`

`Fm:N*Kg=(M*L)/(T^(2))*M=(M^(2)*L)/(T^(2))`

we observe that there are no terms with equal dimensions, that is to say none of the terms are dimensionally homogeneous