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

Answer:

None of the terms are dimensionally homogeneous

Explanation:

$a=xt^{2}-vt+Fm$

dimensions from each term:

$a:\frac{L}{T^{2}}$

$xt^{2}:L*T^{2}$

$vt:\frac{L}{T}*T=L$

$Fm:N*Kg=\frac{M*L}{T^{2}}*M=\frac{M^{2}*L}{T^{2}}$

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